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Statements
𝖰
n
0
(
x
)
=
𝖰
n
(
x
)
=
1
2
P
n
(
x
)
ln
(
1
+
x
1
-
x
)
-
W
n
-
1
(
x
)
,
Ferrers-Legendre-Q-first-kind
0
𝑛
𝑥
shorthand-Ferrers-Legendre-Q-first-kind
𝑛
𝑥
1
2
Legendre-spherical-polynomial
𝑛
𝑥
1
𝑥
1
𝑥
subscript
𝑊
𝑛
1
𝑥
{\displaystyle{\displaystyle\mathsf{Q}^{0}_{n}\left(x\right)=\mathsf{Q}_{n}%
\left(x\right)=\frac{1}{2}P_{n}\left(x\right)\ln\left(\frac{1+x}{1-x}\right)-W%
_{n-1}(x),}}
𝖰
ν
μ
(
x
)
Ferrers-Legendre-Q-first-kind
𝜇
𝜈
𝑥
{\displaystyle{\displaystyle\mathsf{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
P
n
(
x
)
Legendre-spherical-polynomial
𝑛
𝑥
{\displaystyle{\displaystyle P_{\NVar{n}}\left(\NVar{x}\right)}}
ln
z
𝑧
{\displaystyle{\displaystyle\ln\NVar{z}}}
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}}
n
𝑛
{\displaystyle{\displaystyle n}}
W
n
-
1
(
x
)
subscript
𝑊
𝑛
1
𝑥
{\displaystyle{\displaystyle W_{n-1}(x)}}
