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Statements
𝒲
{
P
ν
μ
(
x
)
,
Q
ν
μ
(
x
)
}
=
-
e
μ
π
i
Γ
(
ν
+
μ
+
1
)
Γ
(
ν
-
μ
+
1
)
(
x
2
-
1
)
,
Wronskian
Legendre-P-first-kind
𝜇
𝜈
𝑥
Legendre-Q-second-kind
𝜇
𝜈
𝑥
superscript
𝑒
𝜇
𝜋
𝑖
Euler-Gamma
𝜈
𝜇
1
Euler-Gamma
𝜈
𝜇
1
superscript
𝑥
2
1
{\displaystyle{\displaystyle\mathscr{W}\left\{P^{\mu}_{\nu}\left(x\right),Q^{%
\mu}_{\nu}\left(x\right)\right\}=-e^{\mu\pi i}\frac{\Gamma\left(\nu+\mu+1%
\right)}{\Gamma\left(\nu-\mu+1\right)\left(x^{2}-1\right)},}}
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)}}
Q
ν
μ
(
z
)
Legendre-Q-second-kind
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle Q^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{z}\right)}}
𝒲
Wronskian
{\displaystyle{\displaystyle\mathscr{W}}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
