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Statements
∫
0
π
𝖰
l
(
cos
θ
)
𝖯
m
(
cos
θ
)
𝖯
n
(
cos
θ
)
sin
θ
d
θ
=
0
,
superscript
subscript
0
𝜋
shorthand-Ferrers-Legendre-Q-first-kind
𝑙
𝜃
shorthand-Ferrers-Legendre-P-first-kind
𝑚
𝜃
shorthand-Ferrers-Legendre-P-first-kind
𝑛
𝜃
𝜃
𝜃
0
{\displaystyle{\displaystyle\int_{0}^{\pi}\mathsf{Q}_{l}\left(\cos\theta\right%
)\mathsf{P}_{m}\left(\cos\theta\right)\mathsf{P}_{n}\left(\cos\theta\right)%
\sin\theta\mathrm{d}\theta=0,}}
|
m
-
n
|
<
l
<
m
+
n
𝑚
𝑛
𝑙
𝑚
𝑛
{\displaystyle{\displaystyle|m-n|<l<m+n}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
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)}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
m
𝑚
{\displaystyle{\displaystyle m}}
n
𝑛
{\displaystyle{\displaystyle n}}
Identifiers
