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Statements
J
ν
′
(
z
)
∼
-
(
2
π
z
)
1
2
(
sin
ω
∑
k
=
0
∞
(
-
1
)
k
b
2
k
(
ν
)
z
2
k
+
cos
ω
∑
k
=
0
∞
(
-
1
)
k
b
2
k
+
1
(
ν
)
z
2
k
+
1
)
,
asymptotic-expansion
diffop
Bessel-J
𝜈
1
𝑧
superscript
2
𝜋
𝑧
1
2
𝜔
superscript
subscript
𝑘
0
superscript
1
𝑘
subscript
𝑏
2
𝑘
𝜈
superscript
𝑧
2
𝑘
𝜔
superscript
subscript
𝑘
0
superscript
1
𝑘
subscript
𝑏
2
𝑘
1
𝜈
superscript
𝑧
2
𝑘
1
{\displaystyle{\displaystyle J_{\nu}'\left(z\right)\sim-\left(\frac{2}{\pi z}%
\right)^{\frac{1}{2}}\left(\sin\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{b_{2k}(%
\nu)}{z^{2k}}+\cos\omega\sum_{k=0}^{\infty}(-1)^{k}\frac{b_{2k+1}(\nu)}{z^{2k+%
1}}\right),}}
|
ph
z
|
≤
π
-
δ
phase
𝑧
𝜋
𝛿
{\displaystyle{\displaystyle|\operatorname{ph}z|\leq\pi-\delta}}
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}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
k
𝑘
{\displaystyle{\displaystyle k}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
δ
𝛿
{\displaystyle{\displaystyle\delta}}
ω
𝜔
{\displaystyle{\displaystyle\omega}}
b
k
(
ν
)
subscript
𝑏
𝑘
𝜈
{\displaystyle{\displaystyle b_{k}(\nu)}}
Identifiers
