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Statements
J
ν
(
x
)
=
1
2
π
i
∫
-
i
∞
i
∞
Γ
(
-
t
)
(
1
2
x
)
ν
+
2
t
Γ
(
ν
+
t
+
1
)
d
t
,
Bessel-J
𝜈
𝑥
1
2
𝜋
𝑖
superscript
subscript
𝑖
𝑖
Euler-Gamma
𝑡
superscript
1
2
𝑥
𝜈
2
𝑡
Euler-Gamma
𝜈
𝑡
1
𝑡
{\displaystyle{\displaystyle J_{\nu}\left(x\right)=\frac{1}{2\pi i}\int_{-i%
\infty}^{i\infty}\frac{\Gamma\left(-t\right)(\tfrac{1}{2}x)^{\nu+2t}}{\Gamma%
\left(\nu+t+1\right)}\mathrm{d}t,}}
ℜ
ν
>
0
𝜈
0
{\displaystyle{\displaystyle\Re\nu>0}}
ℜ
ν
>
0
𝜈
0
{\displaystyle{\displaystyle\Re\nu>0}}
x
>
0
𝑥
0
{\displaystyle{\displaystyle x>0}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
x
𝑥
{\displaystyle{\displaystyle x}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
