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Statements
P
ν
μ
(
x
)
∼
Γ
(
-
ν
-
1
2
)
π
1
/
2
Γ
(
-
μ
-
ν
)
(
2
x
)
ν
+
1
,
asymptotically-equals
Legendre-P-first-kind
𝜇
𝜈
𝑥
Euler-Gamma
𝜈
1
2
superscript
𝜋
1
2
Euler-Gamma
𝜇
𝜈
superscript
2
𝑥
𝜈
1
{\displaystyle{\displaystyle P^{\mu}_{\nu}\left(x\right)\sim\frac{\Gamma\left(%
-\nu-\frac{1}{2}\right)}{\pi^{1/2}\Gamma\left(-\mu-\nu\right)(2x)^{\nu+1}},}}
ℜ
ν
<
-
1
2
𝜈
1
2
{\displaystyle{\displaystyle\Re\nu<-\tfrac{1}{2}}}
ℜ
ν
<
-
1
2
𝜈
1
2
{\displaystyle{\displaystyle\Re\nu<-\tfrac{1}{2}}}
ν
+
μ
≠
0
,
1
,
2
,
…
𝜈
𝜇
0
1
2
…
{\displaystyle{\displaystyle\nu+\mu\neq 0,1,2,\dots}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
P
ν
μ
(
z
)
Legendre-P-first-kind
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
∼
asymptotically-equals
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
