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Statements
πΈ
n
-
1
2
m
β‘
(
cosh
β‘
ΞΎ
)
=
Ξ
β‘
(
m
-
n
+
1
2
)
Ξ
β‘
(
m
+
n
+
1
2
)
β’
(
Ο
2
β’
sinh
β‘
ΞΎ
)
1
/
2
β’
P
m
-
1
2
n
β‘
(
coth
β‘
ΞΎ
)
.
associated-Legendre-black-Q
π
π
1
2
π
Euler-Gamma
π
π
1
2
Euler-Gamma
π
π
1
2
superscript
π
2
π
1
2
Legendre-P-first-kind
π
π
1
2
hyperbolic-cotangent
π
{\displaystyle{\displaystyle\boldsymbol{Q}^{m}_{n-\frac{1}{2}}\left(\cosh\xi%
\right)=\frac{\Gamma\left(m-n+\tfrac{1}{2}\right)}{\Gamma\left(m+n+\tfrac{1}{2%
}\right)}\*\left(\frac{\pi}{2\sinh\xi}\right)^{1/2}P^{n}_{m-\frac{1}{2}}\left(%
\coth\xi\right).}}
Ξ
β‘
(
z
)
Euler-Gamma
π§
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
P
Ξ½
ΞΌ
β‘
(
z
)
Legendre-P-first-kind
π
π
π§
{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\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}}
cosh
β‘
z
π§
{\displaystyle{\displaystyle\cosh\NVar{z}}}
coth
β‘
z
hyperbolic-cotangent
π§
{\displaystyle{\displaystyle\coth\NVar{z}}}
sinh
β‘
z
π§
{\displaystyle{\displaystyle\sinh\NVar{z}}}
m
π
{\displaystyle{\displaystyle m}}
n
π
{\displaystyle{\displaystyle n}}
ΞΎ
>
0
π
0
{\displaystyle{\displaystyle\xi>0}}
Identifiers
