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Statements
πΈ
Ξ½
ΞΌ
β‘
(
cosh
β‘
ΞΎ
)
=
Ξ½
ΞΌ
Ξ
β‘
(
Ξ½
+
ΞΌ
+
1
)
β’
(
ΞΎ
sinh
β‘
ΞΎ
)
1
/
2
β’
K
ΞΌ
β‘
(
(
Ξ½
+
1
2
)
β’
ΞΎ
)
β’
(
1
+
O
β‘
(
1
Ξ½
)
)
,
associated-Legendre-black-Q
π
π
π
superscript
π
π
Euler-Gamma
π
π
1
superscript
π
π
1
2
modified-Bessel-second-kind
π
π
1
2
π
1
Big-O
1
π
{\displaystyle{\displaystyle\boldsymbol{Q}^{\mu}_{\nu}\left(\cosh\xi\right)=%
\frac{\nu^{\mu}}{\Gamma\left(\nu+\mu+1\right)}\left(\frac{\xi}{\sinh\xi}\right%
)^{1/2}\*K_{\mu}\left(\left(\nu+\tfrac{1}{2}\right)\xi\right)\*\left(1+O\left(%
\frac{1}{\nu}\right)\right),}}
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)}}
πΈ
Ξ½
ΞΌ
β‘
(
z
)
associated-Legendre-black-Q
π
π
π§
{\displaystyle{\displaystyle\boldsymbol{Q}^{\NVar{\mu}}_{\NVar{\nu}}\left(%
\NVar{z}\right)}}
cosh
β‘
z
π§
{\displaystyle{\displaystyle\cosh\NVar{z}}}
sinh
β‘
z
π§
{\displaystyle{\displaystyle\sinh\NVar{z}}}
K
Ξ½
β‘
(
z
)
modified-Bessel-second-kind
π
π§
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
ΞΌ
π
{\displaystyle{\displaystyle\mu}}
Ξ½
π
{\displaystyle{\displaystyle\nu}}
ΞΎ
π
{\displaystyle{\displaystyle\xi}}
