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DLMF:11.11.E4 - MaRDI portal
Statements
π
Ξ½
β‘
(
z
)
βΌ
1
Ο
β’
z
β’
β
k
=
0
β
F
k
β’
(
Ξ½
)
z
2
β’
k
-
Ξ½
Ο
β’
z
2
β’
β
k
=
0
β
G
k
β’
(
Ξ½
)
z
2
β’
k
.
asymptotic-expansion
associated-Anger-Weber-A
π
π§
1
π
π§
superscript
subscript
π
0
subscript
πΉ
π
π
superscript
π§
2
π
π
π
superscript
π§
2
superscript
subscript
π
0
subscript
πΊ
π
π
superscript
π§
2
π
{\displaystyle{\displaystyle\mathbf{A}_{\nu}\left(z\right)\sim\frac{1}{\pi z}%
\sum_{k=0}^{\infty}\frac{F_{k}(\nu)}{z^{2k}}-\frac{\nu}{\pi z^{2}}\sum_{k=0}^{%
\infty}\frac{G_{k}(\nu)}{z^{2k}}.}}
π
Ξ½
β‘
(
z
)
associated-Anger-Weber-A
π
π§
{\displaystyle{\displaystyle\mathbf{A}_{\NVar{\nu}}\left(\NVar{z}\right)}}
βΌ
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
Ο
{\displaystyle{\displaystyle\pi}}
z
π§
{\displaystyle{\displaystyle z}}
Ξ½
π
{\displaystyle{\displaystyle\nu}}
k
π
{\displaystyle{\displaystyle k}}
F
k
β’
(
Ξ½
)
subscript
πΉ
π
π
{\displaystyle{\displaystyle F_{k}(\nu)}}
G
k
β’
(
Ξ½
)
subscript
πΊ
π
π
{\displaystyle{\displaystyle G_{k}(\nu)}}
Identifiers