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Statements
∂
∂
ν
𝖰
ν
μ
(
x
)
=
-
1
2
π
2
𝖯
ν
μ
(
x
)
+
π
sin
(
μ
π
)
sin
(
ν
π
)
sin
(
(
ν
+
μ
)
π
)
𝖰
ν
μ
(
x
)
-
1
2
cot
(
(
ν
+
μ
)
π
)
𝖠
ν
μ
(
x
)
+
1
2
csc
(
(
ν
+
μ
)
π
)
𝖠
ν
μ
(
-
x
)
,
partial-derivative
𝜈
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
1
2
superscript
𝜋
2
Ferrers-Legendre-P-first-kind
𝜇
𝜈
𝑥
𝜋
𝜇
𝜋
𝜈
𝜋
𝜈
𝜇
𝜋
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
1
2
𝜈
𝜇
𝜋
superscript
subscript
𝖠
𝜈
𝜇
𝑥
1
2
𝜈
𝜇
𝜋
superscript
subscript
𝖠
𝜈
𝜇
𝑥
{\displaystyle{\displaystyle\frac{\partial}{\partial\nu}\mathsf{Q}^{\mu}_{\nu}%
\left(x\right)=-\tfrac{1}{2}\pi^{2}\mathsf{P}^{\mu}_{\nu}\left(x\right)+\frac{%
\pi\sin\left(\mu\pi\right)}{\sin\left(\nu\pi\right)\sin\left((\nu+\mu)\pi%
\right)}\mathsf{Q}^{\mu}_{\nu}\left(x\right)-\tfrac{1}{2}\cot\left((\nu+\mu)%
\pi\right)\mathsf{A}_{\nu}^{\mu}(x)+\tfrac{1}{2}\csc\left((\nu+\mu)\pi\right)%
\mathsf{A}_{\nu}^{\mu}(-x),}}
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}}
csc
z
𝑧
{\displaystyle{\displaystyle\csc\NVar{z}}}
cot
z
𝑧
{\displaystyle{\displaystyle\cot\NVar{z}}}
∂
f
∂
x
partial-derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
∂
x
𝑥
{\displaystyle{\displaystyle\partial\NVar{x}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
𝖠
ν
μ
(
x
)
superscript
subscript
𝖠
𝜈
𝜇
𝑥
{\displaystyle{\displaystyle\mathsf{A}_{\nu}^{\mu}(x)}}
Identifiers
