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Statements
𝖯
ν
+
1
μ
(
x
)
𝖰
ν
μ
(
x
)
-
𝖯
ν
μ
(
x
)
𝖰
ν
+
1
μ
(
x
)
=
Γ
(
ν
+
μ
+
1
)
Γ
(
ν
-
μ
+
2
)
,
Ferrers-Legendre-P-first-kind
𝜇
𝜈
1
𝑥
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
1
𝑥
Euler-Gamma
𝜈
𝜇
1
Euler-Gamma
𝜈
𝜇
2
{\displaystyle{\displaystyle\mathsf{P}^{\mu}_{\nu+1}\left(x\right)\mathsf{Q}^{%
\mu}_{\nu}\left(x\right)-\mathsf{P}^{\mu}_{\nu}\left(x\right)\mathsf{Q}^{\mu}_%
{\nu+1}\left(x\right)=\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
(
x
)
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
𝖰
ν
μ
(
x
)
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
