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Statements
J
ν
(
z
)
=
1
π
∫
0
π
cos
(
z
sin
θ
-
ν
θ
)
d
θ
-
sin
(
ν
π
)
π
∫
0
∞
e
-
z
sinh
t
-
ν
t
d
t
,
Bessel-J
𝜈
𝑧
1
𝜋
superscript
subscript
0
𝜋
𝑧
𝜃
𝜈
𝜃
𝜃
𝜈
𝜋
𝜋
superscript
subscript
0
superscript
𝑒
𝑧
𝑡
𝜈
𝑡
𝑡
{\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{1}{\pi}\int_{0}^{\pi}%
\cos\left(z\sin\theta-\nu\theta\right)\mathrm{d}\theta-\frac{\sin\left(\nu\pi%
\right)}{\pi}\int_{0}^{\infty}e^{-z\sinh t-\nu t}\mathrm{d}t,}}
|
ph
z
|
<
1
2
π
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
∫
{\displaystyle{\displaystyle\int}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
