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Statements
∂
∂
μ
𝖰
ν
μ
(
x
)
|
μ
=
0
=
-
1
4
π
2
𝖯
ν
(
x
)
+
(
ψ
(
-
ν
)
-
π
cot
(
ν
π
)
)
𝖰
ν
(
x
)
.
evaluated-at
partial-derivative
𝜇
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
𝜇
0
1
4
superscript
𝜋
2
shorthand-Ferrers-Legendre-P-first-kind
𝜈
𝑥
digamma
𝜈
𝜋
𝜈
𝜋
shorthand-Ferrers-Legendre-Q-first-kind
𝜈
𝑥
{\displaystyle{\displaystyle\left.\frac{\partial}{\partial\mu}\mathsf{Q}^{\mu}%
_{\nu}\left(x\right)\right|_{\mu=0}=-\tfrac{1}{4}\pi^{2}\mathsf{P}_{\nu}\left(%
x\right)+\left(\psi\left(-\nu\right)-\pi\cot\left(\nu\pi\right)\right)\mathsf{%
Q}_{\nu}\left(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}}
cot
z
𝑧
{\displaystyle{\displaystyle\cot\NVar{z}}}
ψ
(
z
)
digamma
𝑧
{\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
∂
f
∂
x
partial-derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}
∂
x
𝑥
{\displaystyle{\displaystyle\partial\NVar{x}}}
𝖯
ν
(
x
)
=
𝖯
ν
0
(
x
)
shorthand-Ferrers-Legendre-P-first-kind
𝜈
𝑥
Ferrers-Legendre-P-first-kind
0
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{P}_{\NVar{\nu}}\left(\NVar{x}\right)=%
\mathsf{P}^{0}_{\nu}\left(x\right)}}
𝖰
ν
(
x
)
=
𝖰
ν
0
(
x
)
shorthand-Ferrers-Legendre-Q-first-kind
𝜈
𝑥
Ferrers-Legendre-Q-first-kind
0
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{Q}_{\NVar{\nu}}\left(\NVar{x}\right)=%
\mathsf{Q}^{0}_{\nu}\left(x\right)}}
x
𝑥
{\displaystyle{\displaystyle x}}
μ
𝜇
{\displaystyle{\displaystyle\mu}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
