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Statements
πΈ
Ξ½
β‘
(
x
)
=
-
ln
β‘
(
x
-
1
)
2
β’
Ξ
β‘
(
Ξ½
+
1
)
+
1
2
β’
ln
β‘
2
-
Ξ³
-
Ο
β‘
(
Ξ½
+
1
)
Ξ
β‘
(
Ξ½
+
1
)
+
O
β‘
(
x
-
1
)
,
shorthand-associated-Legendre-black-Q
π
π₯
π₯
1
2
Euler-Gamma
π
1
1
2
2
digamma
π
1
Euler-Gamma
π
1
Big-O
π₯
1
{\displaystyle{\displaystyle\boldsymbol{Q}_{\nu}\left(x\right)=-\frac{\ln\left%
(x-1\right)}{2\Gamma\left(\nu+1\right)}+\frac{\frac{1}{2}\ln 2-\gamma-\psi%
\left(\nu+1\right)}{\Gamma\left(\nu+1\right)}+O\left(x-1\right),}}
Ξ½
β
-
1
,
-
2
,
-
3
,
β¦
π
1
2
3
β¦
{\displaystyle{\displaystyle\nu\neq-1,-2,-3,\dots}}
O
β‘
(
x
)
Big-O
π₯
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
Ξ
β‘
(
z
)
Euler-Gamma
π§
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
Ξ³
{\displaystyle{\displaystyle\gamma}}
Ο
β‘
(
z
)
digamma
π§
{\displaystyle{\displaystyle\psi\left(\NVar{z}\right)}}
ln
β‘
z
π§
{\displaystyle{\displaystyle\ln\NVar{z}}}
πΈ
Ξ½
β‘
(
z
)
=
πΈ
Ξ½
0
β‘
(
z
)
shorthand-associated-Legendre-black-Q
π
π§
associated-Legendre-black-Q
0
π
π§
{\displaystyle{\displaystyle\boldsymbol{Q}_{\NVar{\nu}}\left(\NVar{z}\right)=%
\boldsymbol{Q}^{0}_{\nu}\left(z\right)}}
x
π₯
{\displaystyle{\displaystyle x}}
Ξ½
π
{\displaystyle{\displaystyle\nu}}
Identifiers
