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Statements
(
z
+
ζ
z
-
ζ
)
1
2
ν
H
ν
(
2
)
(
(
z
2
-
ζ
2
)
1
2
)
=
-
1
π
i
e
1
2
ν
π
i
∫
-
∞
∞
e
-
i
z
cosh
t
-
i
ζ
sinh
t
-
ν
t
d
t
,
superscript
𝑧
𝜁
𝑧
𝜁
1
2
𝜈
Hankel-H-2-Bessel-third-kind
𝜈
superscript
superscript
𝑧
2
superscript
𝜁
2
1
2
1
𝜋
𝑖
superscript
𝑒
1
2
𝜈
𝜋
𝑖
superscript
subscript
superscript
𝑒
𝑖
𝑧
𝑡
𝑖
𝜁
𝑡
𝜈
𝑡
𝑡
{\displaystyle{\displaystyle\left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}%
\nu}{H^{(2)}_{\nu}}\left((z^{2}-\zeta^{2})^{\frac{1}{2}}\right)=-\frac{1}{\pi i%
}e^{\frac{1}{2}\nu\pi i}\int_{-\infty}^{\infty}e^{-iz\cosh t-i\zeta\sinh t-\nu
t%
}\mathrm{d}t,}}
ℑ
(
z
±
ζ
)
<
0
plus-or-minus
𝑧
𝜁
0
{\displaystyle{\displaystyle\Im(z\pm\zeta)<0}}
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}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
ℑ
absent
{\displaystyle{\displaystyle\Im}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
∫
{\displaystyle{\displaystyle\int}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
