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Statements
𝐉
ν
(
z
)
∼
J
ν
(
z
)
+
sin
(
π
ν
)
π
z
(
∑
k
=
0
∞
F
k
(
ν
)
z
2
k
-
ν
z
∑
k
=
0
∞
G
k
(
ν
)
z
2
k
)
,
asymptotic-expansion
Anger-J
𝜈
𝑧
Bessel-J
𝜈
𝑧
𝜋
𝜈
𝜋
𝑧
superscript
subscript
𝑘
0
subscript
𝐹
𝑘
𝜈
superscript
𝑧
2
𝑘
𝜈
𝑧
superscript
subscript
𝑘
0
subscript
𝐺
𝑘
𝜈
superscript
𝑧
2
𝑘
{\displaystyle{\displaystyle\mathbf{J}_{\nu}\left(z\right)\sim J_{\nu}\left(z%
\right)\\
+\frac{\sin\left(\pi\nu\right)}{\pi z}\left(\sum_{k=0}^{\infty}\frac{F_{k}(\nu%
)}{z^{2k}}-\frac{\nu}{z}\sum_{k=0}^{\infty}\frac{G_{k}(\nu)}{z^{2k}}\right),}}
𝐉
ν
(
z
)
Anger-J
𝜈
𝑧
{\displaystyle{\displaystyle\mathbf{J}_{\NVar{\nu}}\left(\NVar{z}\right)}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
k
𝑘
{\displaystyle{\displaystyle k}}
F
k
(
ν
)
subscript
𝐹
𝑘
𝜈
{\displaystyle{\displaystyle F_{k}(\nu)}}
G
k
(
ν
)
subscript
𝐺
𝑘
𝜈
{\displaystyle{\displaystyle G_{k}(\nu)}}
Identifiers
