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Statements
π
cos
(
ν
π
)
cos
(
μ
π
)
𝖯
ν
μ
(
x
)
=
sin
(
(
ν
+
μ
)
π
)
𝖰
ν
μ
(
x
)
-
sin
(
(
ν
-
μ
)
π
)
𝖰
-
ν
-
1
μ
(
x
)
.
𝜋
𝜈
𝜋
𝜇
𝜋
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
𝜈
𝜇
𝜋
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
𝜈
𝜇
𝜋
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
1
𝑥
{\displaystyle{\displaystyle\pi\cos\left(\nu\pi\right)\cos\left(\mu\pi\right)%
\mathsf{P}^{\mu}_{\nu}\left(x\right)=\sin\left((\nu+\mu)\pi\right)\mathsf{Q}^{%
\mu}_{\nu}\left(x\right)-\sin\left((\nu-\mu)\pi\right)\mathsf{Q}^{\mu}_{-\nu-1%
}\left(x\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)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
