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Statements
𝖯
ν
-
μ
(
x
)
=
1
Γ
(
μ
+
1
)
(
1
-
α
2
)
-
μ
/
2
(
1
-
α
1
+
α
)
(
ν
/
2
)
+
(
1
/
4
)
(
p
x
)
1
/
2
e
-
μ
ρ
(
1
+
O
(
1
μ
)
)
,
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
1
Euler-Gamma
𝜇
1
superscript
1
superscript
𝛼
2
𝜇
2
superscript
1
𝛼
1
𝛼
𝜈
2
1
4
superscript
𝑝
𝑥
1
2
superscript
𝑒
𝜇
𝜌
1
Big-O
1
𝜇
{\displaystyle{\displaystyle\mathsf{P}^{-\mu}_{\nu}\left(x\right)=\frac{1}{%
\Gamma\left(\mu+1\right)}\left(1-\alpha^{2}\right)^{-\mu/2}\left(\frac{1-%
\alpha}{1+\alpha}\right)^{(\nu/2)+(1/4)}\*\left(\frac{p}{x}\right)^{1/2}e^{-%
\mu\rho}\left(1+O\left(\frac{1}{\mu}\right)\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
𝖯
ν
μ
(
x
)
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
p
𝑝
{\displaystyle{\displaystyle p}}
ρ
𝜌
{\displaystyle{\displaystyle\rho}}
Identifiers
