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Statements
πΈ
Ξ½
ΞΌ
β‘
(
x
)
=
2
Ξ½
β’
Ξ
β‘
(
Ξ½
+
1
)
β’
(
x
+
1
)
ΞΌ
/
2
(
x
-
1
)
(
ΞΌ
/
2
)
+
Ξ½
+
1
β’
π
β‘
(
Ξ½
+
1
,
Ξ½
+
ΞΌ
+
1
;
2
β’
Ξ½
+
2
;
2
1
-
x
)
,
associated-Legendre-black-Q
π
π
π₯
superscript
2
π
Euler-Gamma
π
1
superscript
π₯
1
π
2
superscript
π₯
1
π
2
π
1
scaled-hypergeometric-bold-F
π
1
π
π
1
2
π
2
2
1
π₯
{\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(x\right)=\frac{2^{%
\nu}\Gamma\left(\nu+1\right)(x+1)^{\mu/2}}{(x-1)^{(\mu/2)+\nu+1}}\mathbf{F}%
\left(\nu+1,\nu+\mu+1;2\nu+2;\frac{2}{1-x}\right),}}
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)}}
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)}}
x
π₯
{\displaystyle{\displaystyle x}}
ΞΌ
π
{\displaystyle{\displaystyle\mu}}
Ξ½
π
{\displaystyle{\displaystyle\nu}}
