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Statements
πΈ
n
-
1
2
m
β‘
(
cosh
β‘
ΞΎ
)
=
Ξ
β‘
(
n
+
1
2
)
Ξ
β‘
(
n
+
m
+
1
2
)
β’
Ξ
β‘
(
n
-
m
+
1
2
)
β’
β«
0
β
cosh
β‘
(
m
β’
t
)
(
cosh
β‘
ΞΎ
+
cosh
β‘
t
β’
sinh
β‘
ΞΎ
)
n
+
(
1
/
2
)
β’
d
t
,
associated-Legendre-black-Q
π
π
1
2
π
Euler-Gamma
π
1
2
Euler-Gamma
π
π
1
2
Euler-Gamma
π
π
1
2
superscript
subscript
0
π
π‘
superscript
π
π‘
π
π
1
2
π‘
{\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n-\frac{1}{2}}\left(\cosh\xi%
\right)=\frac{\Gamma\left(n+\frac{1}{2}\right)}{\Gamma\left(n+m+\tfrac{1}{2}%
\right)\Gamma\left(n-m+\frac{1}{2}\right)}\*\int_{0}^{\infty}\frac{\cosh\left(%
mt\right)}{(\cosh\xi+\cosh t\sinh\xi)^{n+(1/2)}}\mathrm{d}t,}}
m
<
n
+
1
2
π
π
1
2
{\displaystyle{\displaystyle m<n+\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)}}
d
x
π₯
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
cosh
β‘
z
π§
{\displaystyle{\displaystyle\cosh\NVar{z}}}
sinh
β‘
z
π§
{\displaystyle{\displaystyle\sinh\NVar{z}}}
β«
{\displaystyle{\displaystyle\int}}
m
π
{\displaystyle{\displaystyle m}}
n
π
{\displaystyle{\displaystyle n}}
ΞΎ
>
0
π
0
{\displaystyle{\displaystyle\xi>0}}
Identifiers
