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Statements
I
ν
(
z
)
=
1
2
e
∓
ν
π
i
/
2
(
H
ν
(
1
)
(
z
e
±
π
i
/
2
)
+
H
ν
(
2
)
(
z
e
±
π
i
/
2
)
)
,
modified-Bessel-first-kind
𝜈
𝑧
1
2
superscript
𝑒
minus-or-plus
𝜈
𝜋
𝑖
2
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
superscript
𝑒
plus-or-minus
𝜋
𝑖
2
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
superscript
𝑒
plus-or-minus
𝜋
𝑖
2
{\displaystyle{\displaystyle I_{\nu}\left(z\right)=\tfrac{1}{2}e^{\mp\nu\pi i/%
2}\left({H^{(1)}_{\nu}}\left(ze^{\pm\pi i/2}\right)+{H^{(2)}_{\nu}}\left(ze^{%
\pm\pi i/2}\right)\right),}}
-
π
≤
±
ph
z
≤
1
2
π
𝜋
plus-or-minus
phase
𝑧
1
2
𝜋
{\displaystyle{\displaystyle-\pi\leq\pm\operatorname{ph}z\leq\tfrac{1}{2}\pi}}
H
ν
(
1
)
(
z
)
Hankel-H-1-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(1)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
H
ν
(
2
)
(
z
)
Hankel-H-2-Bessel-third-kind
𝜈
𝑧
{\displaystyle{\displaystyle{H^{(2)}_{\NVar{\nu}}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
ph
phase
{\displaystyle{\displaystyle\operatorname{ph}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
