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Statements
(
ν
+
1
)
m
𝑸
ν
m
(
x
)
=
(
-
1
)
m
(
x
2
-
1
)
m
/
2
d
m
𝑸
ν
(
x
)
d
x
m
.
Pochhammer
𝜈
1
𝑚
associated-Legendre-black-Q
𝑚
𝜈
𝑥
superscript
1
𝑚
superscript
superscript
𝑥
2
1
𝑚
2
derivative
shorthand-associated-Legendre-black-Q
𝜈
𝑥
𝑥
𝑚
{\displaystyle{\displaystyle{\left(\nu+1\right)_{m}}\boldsymbol{Q}^{m}_{\nu}%
\left(x\right)=(-1)^{m}\left(x^{2}-1\right)^{m/2}\frac{{\mathrm{d}}^{m}%
\boldsymbol{Q}_{\nu}\left(x\right)}{{\mathrm{d}x}^{m}}.}}
(
a
)
n
Pochhammer
𝑎
𝑛
{\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
𝑸
ν
μ
(
z
)
associated-Legendre-black-Q
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(%
\NVar{z}\right)}}
d
f
d
x
derivative
𝑓
𝑥
{\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
𝑸
ν
(
z
)
=
𝑸
ν
0
(
z
)
shorthand-associated-Legendre-black-Q
𝜈
𝑧
associated-Legendre-black-Q
0
𝜈
𝑧
{\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=%
\boldsymbol{Q}^{0}_{\nu}\left(z\right)}}
x
𝑥
{\displaystyle{\displaystyle x}}
m
𝑚
{\displaystyle{\displaystyle m}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
