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Statements
πΈ
-
1
2
ΞΌ
β‘
(
cosh
β‘
ΞΎ
)
+
2
β’
β
n
=
1
β
Ξ
β‘
(
ΞΌ
+
n
+
1
2
)
Ξ
β‘
(
ΞΌ
+
1
2
)
β’
πΈ
n
-
1
2
ΞΌ
β‘
(
cosh
β‘
ΞΎ
)
β’
cos
β‘
(
n
β’
Ο
)
=
(
1
2
β’
Ο
)
1
/
2
β’
(
sinh
β‘
ΞΎ
)
ΞΌ
(
cosh
β‘
ΞΎ
-
cos
β‘
Ο
)
ΞΌ
+
(
1
/
2
)
,
associated-Legendre-black-Q
π
1
2
π
2
superscript
subscript
π
1
Euler-Gamma
π
π
1
2
Euler-Gamma
π
1
2
associated-Legendre-black-Q
π
π
1
2
π
π
italic-Ο
superscript
1
2
π
1
2
superscript
π
π
superscript
π
italic-Ο
π
1
2
{\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{-\frac{1}{2}}\left(\cosh\xi%
\right)+2\sum_{n=1}^{\infty}\frac{\Gamma\left(\mu+n+\tfrac{1}{2}\right)}{%
\Gamma\left(\mu+\tfrac{1}{2}\right)}\boldsymbol{Q}^{\mu}_{n-\frac{1}{2}}\left(%
\cosh\xi\right)\cos\left(n\phi\right)=\dfrac{\left(\frac{1}{2}\pi\right)^{1/2}%
\left(\sinh\xi\right)^{\mu}}{\left(\cosh\xi-\cos\phi\right)^{\mu+(1/2)}},}}
β
β‘
ΞΌ
>
-
1
2
π
1
2
{\displaystyle{\displaystyle\Re\mu>-\tfrac{1}{2}}}
Ξ
β‘
(
z
)
Euler-Gamma
π§
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
πΈ
Ξ½
ΞΌ
β‘
(
z
)
associated-Legendre-black-Q
π
π
π§
{\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(%
\NVar{z}\right)}}
Ο
{\displaystyle{\displaystyle\pi}}
cos
β‘
z
π§
{\displaystyle{\displaystyle\cos\NVar{z}}}
cosh
β‘
z
π§
{\displaystyle{\displaystyle\cosh\NVar{z}}}
sinh
β‘
z
π§
{\displaystyle{\displaystyle\sinh\NVar{z}}}
β
β‘
absent
{\displaystyle{\displaystyle\Re}}
n
π
{\displaystyle{\displaystyle n}}
ΞΌ
π
{\displaystyle{\displaystyle\mu}}
ΞΎ
>
0
π
0
{\displaystyle{\displaystyle\xi>0}}
Identifiers
