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Statements
πΈ
Ξ½
-
1
2
ΞΌ
β‘
(
cosh
β‘
ΞΎ
)
=
Ο
1
/
2
β’
(
1
-
e
-
2
β’
ΞΎ
)
ΞΌ
e
(
Ξ½
+
(
1
/
2
)
)
β’
ΞΎ
β’
π
β‘
(
ΞΌ
+
1
2
,
Ξ½
+
ΞΌ
+
1
2
;
Ξ½
+
1
;
e
-
2
β’
ΞΎ
)
.
associated-Legendre-black-Q
π
π
1
2
π
superscript
π
1
2
superscript
1
superscript
π
2
π
π
superscript
π
π
1
2
π
scaled-hypergeometric-bold-F
π
1
2
π
π
1
2
π
1
superscript
π
2
π
{\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu-\frac{1}{2}}\left(\cosh%
\xi\right)=\frac{\pi^{1/2}\left(1-e^{-2\xi}\right)^{\mu}}{e^{(\nu+(1/2))\xi}}%
\*\mathbf{F}\left(\mu+\tfrac{1}{2},\nu+\mu+\tfrac{1}{2};\nu+1;e^{-2\xi}\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}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
cosh
β‘
z
π§
{\displaystyle{\displaystyle\cosh\NVar{z}}}
π
β‘
(
a
,
b
;
c
;
z
)
scaled-hypergeometric-bold-F
π
π
π
π§
{\displaystyle{\displaystyle\mathbf{F}\left(\NVar{a},\NVar{b};\NVar{c};\NVar{z%
}\right)}}
ΞΌ
π
{\displaystyle{\displaystyle\mu}}
Ξ½
π
{\displaystyle{\displaystyle\nu}}
ΞΎ
>
0
π
0
{\displaystyle{\displaystyle\xi>0}}
