Test für eine Benutzervorlage :-)
Ich habe eine Vorlage für Tastatureingaben gemacht. Man drücke einfach
Ctrl +
Q .
Aufgesammelte Bausteine, die man vielleicht mal in Diskussionen benutzen kann. ;-)
Bearbeiten
Diesem Benutzer ist offensichtlich langweilig .
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Sie werden von mir und anderen Mitarbeitern beobachtet !
Mit freundlichen Grüßen, ~~~~
Nettes Bild von/für arrogante, löschwütige Wikipedia-Admins:
x
y
z
123
→
a
b
c
{\displaystyle xyz\ {}_{\overrightarrow {{}^{123}}}\ abc}
Für
(
2
3
)
{\displaystyle \textstyle {2 \choose 3}}
(
2
3
)
{\displaystyle {2 \choose 3}}
Ebenso
(
x
y
z
v
)
≠
(
x
y
z
v
)
{\displaystyle \textstyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}\neq {\begin{pmatrix}x&y\\z&v\end{pmatrix}}}
[0] :
ξ
0
:=
1
2
{\displaystyle \xi _{0}:={\frac {1}{2}}}
[1] :
ξ
1
:=
2
⋅
(
1
1
)
⋅
(
2
1
)
⋅
1
+
2
1
⋅
2
1
+
2
1
{\displaystyle \xi _{1}:={\frac {2\cdot {1 \choose 1}\cdot {2 \choose 1}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}{\sqrt {1+{\frac {2}{1}}}}}}
[2] :
ξ
2
:=
2
⋅
(
1
1
)
⋅
(
2
1
)
⋅
1
+
2
+
2
1
2
⋅
(
1
2
)
⋅
(
5
2
)
⋅
(
17
2
)
⋅
1
+
2
1
⋅
2
⋅
2
+
2
1
1
+
2
+
2
1
2
⋅
(
1
2
)
⋅
(
5
2
)
⋅
(
17
2
)
⋅
1
+
2
1
⋅
2
{\displaystyle \xi _{2}:={\frac {2\cdot {1 \choose 1}\cdot {2 \choose 1}\cdot {\frac {1+{\sqrt {2+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 2}\cdot {5 \choose 2}\cdot {17 \choose 2}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {2+{\frac {2}{1}}}}}}}}{\sqrt {1+{\frac {\sqrt {2+{\frac {2}{1}}}}{2\cdot {1 \choose 2}\cdot {5 \choose 2}\cdot {17 \choose 2}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}
[3] :
ξ
3
:=
2
⋅
(
1
1
)
⋅
(
2
1
)
⋅
1
+
2
+
3
+
2
1
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
2
)
⋅
(
5
2
)
⋅
(
17
2
)
⋅
1
+
3
+
2
1
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
2
1
⋅
2
⋅
3
+
2
1
⋅
2
+
3
+
2
1
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
2
1
⋅
2
1
+
2
+
3
+
2
1
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
2
)
⋅
(
5
2
)
⋅
(
17
2
)
⋅
1
+
3
+
2
1
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
2
1
⋅
2
⋅
3
+
2
1
{\displaystyle \xi _{3}:={\frac {2\cdot {1 \choose 1}\cdot {2 \choose 1}\cdot {\frac {1+{\sqrt {2+{\frac {\sqrt {3+{\frac {2}{1}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 2}\cdot {5 \choose 2}\cdot {17 \choose 2}\cdot {\frac {1+{\sqrt {3+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {3+{\frac {2}{1}}}}}}}\cdot {\sqrt {2+{\frac {\sqrt {3+{\frac {2}{1}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}{\sqrt {1+{\frac {\sqrt {2+{\frac {\sqrt {3+{\frac {2}{1}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 2}\cdot {5 \choose 2}\cdot {17 \choose 2}\cdot {\frac {1+{\sqrt {3+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {3+{\frac {2}{1}}}}}}}}}}}}}
[4] :
ξ
4
:=
2
⋅
(
1
1
)
⋅
(
2
1
)
⋅
1
+
2
+
3
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
⋅
4
+
2
1
2
⋅
(
1
2
)
⋅
(
5
2
)
⋅
(
17
2
)
⋅
1
+
3
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
⋅
4
+
2
1
⋅
3
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
⋅
2
+
3
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
⋅
4
+
2
1
1
+
2
+
3
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
⋅
4
+
2
1
2
⋅
(
1
2
)
⋅
(
5
2
)
⋅
(
17
2
)
⋅
1
+
3
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
⋅
4
+
2
1
⋅
3
+
4
+
2
1
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
2
1
⋅
2
{\displaystyle \xi _{4}:={\frac {2\cdot {1 \choose 1}\cdot {2 \choose 1}\cdot {\frac {1+{\sqrt {2+{\frac {\sqrt {3+{\frac {\sqrt {4+{\frac {2}{1}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {4+{\frac {2}{1}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 2}\cdot {5 \choose 2}\cdot {17 \choose 2}\cdot {\frac {1+{\sqrt {3+{\frac {\sqrt {4+{\frac {2}{1}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {4+{\frac {2}{1}}}}}}}\cdot {\sqrt {3+{\frac {\sqrt {4+{\frac {2}{1}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}\cdot {\sqrt {2+{\frac {\sqrt {3+{\frac {\sqrt {4+{\frac {2}{1}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {4+{\frac {2}{1}}}}}}}}}}}}}}}{\sqrt {1+{\frac {\sqrt {2+{\frac {\sqrt {3+{\frac {\sqrt {4+{\frac {2}{1}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {4+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 2}\cdot {5 \choose 2}\cdot {17 \choose 2}\cdot {\frac {1+{\sqrt {3+{\frac {\sqrt {4+{\frac {2}{1}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {4+{\frac {2}{1}}}}}}}\cdot {\sqrt {3+{\frac {\sqrt {4+{\frac {2}{1}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}}}
[5] :
ξ
5
:=
2
⋅
(
1
1
)
⋅
(
2
1
)
⋅
1
+
2
+
3
+
4
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
⋅
5
+
2
1
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
4
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
⋅
5
+
2
1
⋅
4
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
2
)
⋅
(
5
2
)
⋅
(
17
2
)
⋅
1
+
3
+
4
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
⋅
5
+
2
1
2
⋅
(
1
3
)
⋅
(
10
3
)
⋅
(
37
3
)
⋅
(
82
3
)
⋅
1
+
4
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
⋅
5
+
2
1
⋅
4
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
⋅
3
+
4
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
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(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
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2
2
⋅
(
1
4
)
⋅
(
17
4
)
⋅
(
65
4
)
⋅
(
145
4
)
⋅
(
257
4
)
⋅
1
+
5
+
2
1
2
⋅
(
1
5
)
⋅
(
26
5
)
⋅
(
101
5
)
⋅
(
226
5
)
⋅
(
401
5
)
⋅
(
626
5
)
⋅
1
+
2
1
⋅
2
⋅
5
+
2
1
⋅
2
+
3
+
4
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1
{\displaystyle \xi _{5}:={\frac {2\cdot {1 \choose 1}\cdot {2 \choose 1}\cdot {\frac {1+{\sqrt {2+{\frac {\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}\cdot {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 2}\cdot {5 \choose 2}\cdot {17 \choose 2}\cdot {\frac {1+{\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}\cdot {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}\cdot {\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}}}}}}}}\cdot {\sqrt {2+{\frac {\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}\cdot {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}}}}}{\sqrt {1+{\frac {\sqrt {2+{\frac {\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}\cdot {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}{2\cdot {1 \choose 2}\cdot {5 \choose 2}\cdot {17 \choose 2}\cdot {\frac {1+{\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}\cdot {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}\cdot {\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {2}{1}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {5+{\frac {2}{1}}}}}}}}}}}}}}}}}}}}
[6] :
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{\displaystyle \xi _{6}:={\frac {2\cdot {1 \choose 1}\cdot {2 \choose 1}\cdot {\frac {1+{\sqrt {2+{\frac {\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}\cdot {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 2}\cdot {5 \choose 2}\cdot {17 \choose 2}\cdot {\frac {1+{\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}\cdot {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}}}}\cdot {\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}}}}\cdot {\sqrt {2+{\frac {\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}\cdot {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}}}}}}}}}}}}{\sqrt {1+{\frac {\sqrt {2+{\frac {\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}{2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}\cdot {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}}}}}}}}{2\cdot {1 \choose 2}\cdot {5 \choose 2}\cdot {17 \choose 2}\cdot {\frac {1+{\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 3}\cdot {10 \choose 3}\cdot {37 \choose 3}\cdot {82 \choose 3}\cdot {\frac {1+{\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}}{\sqrt {2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}\cdot {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}}}}\cdot {\sqrt {3+{\frac {\sqrt {4+{\frac {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}{2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}}}}}{2\cdot {1 \choose 4}\cdot {17 \choose 4}\cdot {65 \choose 4}\cdot {145 \choose 4}\cdot {257 \choose 4}\cdot {\frac {1+{\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}{\sqrt {2\cdot {1 \choose 5}\cdot {26 \choose 5}\cdot {101 \choose 5}\cdot {226 \choose 5}\cdot {401 \choose 5}\cdot {626 \choose 5}\cdot {\frac {1+{\sqrt {6+{\frac {2}{1}}}}}{\sqrt {2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}\cdot {\sqrt {6+{\frac {2}{1}}}}}}}\cdot {\sqrt {5+{\frac {\sqrt {6+{\frac {2}{1}}}}{2\cdot {1 \choose 6}\cdot {37 \choose 6}\cdot {145 \choose 6}\cdot {325 \choose 6}\cdot {577 \choose 6}\cdot {901 \choose 6}\cdot {1297 \choose 6}\cdot {\frac {1+2}{\sqrt {1\cdot 2}}}}}}}}}}}}}}}}}}}}}}}
ξ
10
=
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{\displaystyle \xi _{10}=\ ?}
A) Hinprojektion:
x
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a
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λ
+
b
⋅
λ
⋅
cos
(
φ
)
y
=
c
⋅
φ
+
d
⋅
φ
⋅
cos
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λ
)
{\displaystyle x=a\cdot \lambda +b\cdot \lambda \cdot \cos(\varphi )\qquad y=c\cdot \varphi +d\cdot \varphi \cdot \cos(\lambda )}
λ
=
f
λ
(
x
,
y
)
φ
=
f
φ
(
x
,
y
)
{\displaystyle \lambda =f_{\lambda }(x,y)\qquad \varphi =f_{\varphi }(x,y)\,}
Daraus soll man nun die Rückprojektion finden:
λ
=
x
a
+
b
⋅
cos
(
φ
)
φ
=
y
c
+
d
⋅
cos
(
λ
)
{\displaystyle \lambda ={\frac {x}{a+b\cdot \cos(\varphi )}}\qquad \varphi ={\frac {y}{c+d\cdot \cos(\lambda )}}}
λ
=
x
a
+
b
⋅
cos
(
y
c
+
d
⋅
cos
(
λ
)
)
φ
=
y
c
+
d
⋅
cos
(
x
a
+
b
⋅
cos
(
φ
)
)
{\displaystyle \lambda ={\frac {x}{a+b\cdot \cos \left({\frac {y}{c+d\cdot \cos(\lambda )}}\right)}}\qquad \varphi ={\frac {y}{c+d\cdot \cos \left({\frac {x}{a+b\cdot \cos(\varphi )}}\right)}}}
b
h
1
=
e
1
{\displaystyle {\frac {b}{h_{1}}}={\dfrac {e}{1}}}
⟺
{\displaystyle \ \Longleftrightarrow \ }
h
1
=
b
e
{\displaystyle h_{1}={\frac {b}{e}}}
(
1
)
{\displaystyle (1)\,}
b
h
2
=
b
−
e
1
{\displaystyle {\dfrac {b}{h_{2}}}={\dfrac {b-e}{1}}}
⟺
{\displaystyle \Longleftrightarrow }
h
2
=
b
b
−
e
{\displaystyle h_{2}={\frac {b}{b-e}}}
(
2
)
{\displaystyle (2)\,}
3
2
=
9
=
h
1
2
+
b
2
{\displaystyle 3^{2}=9=h_{1}^{2}+b^{2}}
(
3
)
{\displaystyle (3)\,}
2
2
=
4
=
h
2
2
+
b
2
{\displaystyle 2^{2}=4=h_{2}^{2}+b^{2}}
(
4
)
{\displaystyle (4)\,}
5
=
h
1
2
−
h
2
2
{\displaystyle 5=h_{1}^{2}-h_{2}^{2}}
(
5
)
:
(
3
)
−
(
4
)
{\displaystyle (5):(3)-(4)\,}
5
=
(
b
e
)
2
−
(
b
b
−
e
)
2
{\displaystyle 5=\left({\frac {b}{e}}\right)^{2}-\left({\frac {b}{b-e}}\right)^{2}}
(
6
)
:
(
1
)
u
n
d
(
2
)
i
n
(
5
)
{\displaystyle (6):\mathrm {(1)\,und\,(2)\,in\,(5)} \,}
5
=
b
2
e
2
−
b
2
(
b
−
e
)
2
=
b
2
e
2
−
b
2
b
2
−
2
b
e
+
e
2
{\displaystyle 5={\frac {b^{2}}{e^{2}}}-{\frac {b^{2}}{(b-e)^{2}}}\ =\ {\frac {b^{2}}{e^{2}}}-{\frac {b^{2}}{b^{2}-2\,b\,e+e^{2}}}}
(
7
)
{\displaystyle (7)\,}
f
(
−
1
)
=
0
{\displaystyle f(-1)=0}
f
(
0
)
=
1
{\displaystyle f(0)=1}
∀
x
>
−
1
:
f
(
x
)
>
0
{\displaystyle \forall x>-1:f(x)>0}
∀
x
>
0
:
f
′
(
x
)
<
0
{\displaystyle \forall x>0:f'(x)<0}
f
′
(
0
)
=
0
{\displaystyle f'(0)=0}
∀
x
<
0
:
f
′
(
x
)
>
0
{\displaystyle \forall x<0:f'(x)>0}
lim
x
→
−
1
f
′
(
x
)
=
+
∞
{\displaystyle \lim _{x\to -1}f'(x)=+\infty }
f
″
(
1
)
=
0
{\displaystyle f''(1)=0}
