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Statements
P
ν
-
μ
(
x
)
=
β
(
α
2
-
y
x
2
-
1
+
α
2
)
1
/
4
I
μ
(
(
ν
+
1
2
)
|
y
|
1
/
2
)
(
1
+
O
(
1
ν
)
)
,
Legendre-P-first-kind
𝜇
𝜈
𝑥
𝛽
superscript
superscript
𝛼
2
𝑦
superscript
𝑥
2
1
superscript
𝛼
2
1
4
modified-Bessel-first-kind
𝜇
𝜈
1
2
superscript
𝑦
1
2
1
Big-O
1
𝜈
{\displaystyle{\displaystyle P^{-\mu}_{\nu}\left(x\right)=\beta\left(\frac{%
\alpha^{2}-y}{x^{2}-1+\alpha^{2}}\right)^{1/4}I_{\mu}\left(\left(\nu+\tfrac{1}%
{2}\right)|y|^{1/2}\right)\*\left(1+O\left(\frac{1}{\nu}\right)\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
P
ν
μ
(
z
)
Legendre-P-first-kind
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
β
𝛽
{\displaystyle{\displaystyle\beta}}
y
𝑦
{\displaystyle{\displaystyle y}}
α
𝛼
{\displaystyle{\displaystyle\alpha}}
Identifiers
