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Statements
J
ν
(
z
)
J
ν
(
ζ
)
=
1
2
π
i
∫
c
-
i
∞
c
+
i
∞
exp
(
1
2
t
-
z
2
+
ζ
2
2
t
)
I
ν
(
z
ζ
t
)
d
t
t
,
Bessel-J
𝜈
𝑧
Bessel-J
𝜈
𝜁
1
2
𝜋
𝑖
superscript
subscript
𝑐
𝑖
𝑐
𝑖
1
2
𝑡
superscript
𝑧
2
superscript
𝜁
2
2
𝑡
modified-Bessel-first-kind
𝜈
𝑧
𝜁
𝑡
𝑡
𝑡
{\displaystyle{\displaystyle J_{\nu}\left(z\right)J_{\nu}\left(\zeta\right)=%
\frac{1}{2\pi i}\int_{c-i\infty}^{c+i\infty}\*\exp\left(\frac{1}{2}t-\frac{z^{%
2}+\zeta^{2}}{2t}\right)I_{\nu}\left(\frac{z\zeta}{t}\right)\frac{\mathrm{d}t}%
{t},}}
ℜ
ν
>
-
1
𝜈
1
{\displaystyle{\displaystyle\Re\nu>-1}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
exp
z
𝑧
{\displaystyle{\displaystyle\exp\NVar{z}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
c
𝑐
{\displaystyle{\displaystyle c}}
Identifiers
