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Statements
J
ν
(
z
)
=
Γ
(
1
2
-
ν
)
(
1
2
z
)
ν
π
3
2
i
∫
0
(
1
+
)
cos
(
z
t
)
(
t
2
-
1
)
ν
-
1
2
d
t
,
Bessel-J
𝜈
𝑧
Euler-Gamma
1
2
𝜈
superscript
1
2
𝑧
𝜈
superscript
𝜋
3
2
𝑖
superscript
subscript
0
limit-from
1
𝑧
𝑡
superscript
superscript
𝑡
2
1
𝜈
1
2
𝑡
{\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{\Gamma\left(\frac{1}{%
2}-\nu\right)(\frac{1}{2}z)^{\nu}}{\pi^{\frac{3}{2}}i}\int_{0}^{(1+)}\cos\left%
(zt\right)(t^{2}-1)^{\nu-\frac{1}{2}}\mathrm{d}t,}}
ν
≠
1
2
,
3
2
,
…
𝜈
1
2
3
2
…
{\displaystyle{\displaystyle\nu\neq\tfrac{1}{2},\tfrac{3}{2},\ldots}}
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}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
