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Statements
P
ν
+
1
μ
(
x
)
Q
ν
μ
(
x
)
-
P
ν
μ
(
x
)
Q
ν
+
1
μ
(
x
)
=
e
μ
π
i
Γ
(
ν
+
μ
+
1
)
Γ
(
ν
-
μ
+
2
)
.
Legendre-P-first-kind
𝜇
𝜈
1
𝑥
Legendre-Q-second-kind
𝜇
𝜈
𝑥
Legendre-P-first-kind
𝜇
𝜈
𝑥
Legendre-Q-second-kind
𝜇
𝜈
1
𝑥
superscript
𝑒
𝜇
𝜋
𝑖
Euler-Gamma
𝜈
𝜇
1
Euler-Gamma
𝜈
𝜇
2
{\displaystyle{\displaystyle P^{\mu}_{\nu+1}\left(x\right)Q^{\mu}_{\nu}\left(x%
\right)-P^{\mu}_{\nu}\left(x\right)Q^{\mu}_{\nu+1}\left(x\right)=e^{\mu\pi i}%
\frac{\Gamma\left(\nu+\mu+1\right)}{\Gamma\left(\nu-\mu+2\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)}}
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}}
Identifiers
