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Statements
J
ν
(
z
)
=
e
∓
(
2
ν
+
1
)
π
i
/
4
2
2
ν
Γ
(
ν
+
1
)
(
2
z
)
-
1
2
M
0
,
ν
(
±
2
i
z
)
,
Bessel-J
𝜈
𝑧
superscript
𝑒
minus-or-plus
2
𝜈
1
𝜋
𝑖
4
superscript
2
2
𝜈
Euler-Gamma
𝜈
1
superscript
2
𝑧
1
2
Whittaker-confluent-hypergeometric-M
0
𝜈
plus-or-minus
2
𝑖
𝑧
{\displaystyle{\displaystyle J_{\nu}\left(z\right)=\frac{e^{\mp(2\nu+1)\pi i/4%
}}{2^{2\nu}\Gamma\left(\nu+1\right)}(2z)^{-\frac{1}{2}}M_{0,\nu}\left(\pm 2iz%
\right),}}
2
ν
≠
-
1
,
-
2
,
-
3
,
…
2
𝜈
1
2
3
…
{\displaystyle{\displaystyle 2\nu\neq-1,-2,-3,\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)}}
M
κ
,
μ
(
z
)
Whittaker-confluent-hypergeometric-M
𝜅
𝜇
𝑧
{\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
