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Statements
𝒲
{
P
ν
-
μ
(
x
)
,
P
ν
μ
(
x
)
}
=
𝒲
{
𝖯
ν
-
μ
(
x
)
,
𝖯
ν
μ
(
x
)
}
=
2
sin
(
μ
π
)
π
(
1
-
x
2
)
,
Wronskian
Legendre-P-first-kind
𝜇
𝜈
𝑥
Legendre-P-first-kind
𝜇
𝜈
𝑥
Wronskian
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
2
𝜇
𝜋
𝜋
1
superscript
𝑥
2
{\displaystyle{\displaystyle\mathscr{W}\left\{P^{-\mu}_{\nu}\left(x\right),P^{%
\mu}_{\nu}\left(x\right)\right\}=\mathscr{W}\left\{\mathsf{P}^{-\mu}_{\nu}%
\left(x\right),\mathsf{P}^{\mu}_{\nu}\left(x\right)\right\}=\frac{2\sin\left(%
\mu\pi\right)}{\pi\left(1-x^{2}\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)}}
P
ν
μ
(
z
)
Legendre-P-first-kind
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle P^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
𝒲
Wronskian
{\displaystyle{\displaystyle\mathscr{W}}}
π
{\displaystyle{\displaystyle\pi}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
