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Statements
(
z
+
ζ
z
-
ζ
)
1
2
ν
Y
ν
(
(
z
2
-
ζ
2
)
1
2
)
=
1
π
∫
0
π
e
ζ
cos
θ
sin
(
z
sin
θ
-
ν
θ
)
d
θ
-
1
π
∫
0
∞
(
e
ν
t
+
ζ
cosh
t
+
e
-
ν
t
-
ζ
cosh
t
cos
(
ν
π
)
)
e
-
z
sinh
t
d
t
,
superscript
𝑧
𝜁
𝑧
𝜁
1
2
𝜈
Bessel-Y-Weber
𝜈
superscript
superscript
𝑧
2
superscript
𝜁
2
1
2
1
𝜋
superscript
subscript
0
𝜋
superscript
𝑒
𝜁
𝜃
𝑧
𝜃
𝜈
𝜃
𝜃
1
𝜋
superscript
subscript
0
superscript
𝑒
𝜈
𝑡
𝜁
𝑡
superscript
𝑒
𝜈
𝑡
𝜁
𝑡
𝜈
𝜋
superscript
𝑒
𝑧
𝑡
𝑡
{\displaystyle{\displaystyle\left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}%
\nu}Y_{\nu}\left((z^{2}-\zeta^{2})^{\frac{1}{2}}\right)=\frac{1}{\pi}\int_{0}^%
{\pi}e^{\zeta\cos\theta}\sin\left(z\sin\theta-\nu\theta\right)\mathrm{d}\theta%
-\frac{1}{\pi}\int_{0}^{\infty}\left(e^{\nu t+\zeta\cosh t}+e^{-\nu t-\zeta%
\cosh t}\cos\left(\nu\pi\right)\right)\*e^{-z\sinh t}\mathrm{d}t,}}
ℜ
(
z
±
ζ
)
>
0
plus-or-minus
𝑧
𝜁
0
{\displaystyle{\displaystyle\Re(z\pm\zeta)>0}}
Y
ν
(
z
)
Bessel-Y-Weber
𝜈
𝑧
{\displaystyle{\displaystyle Y_{\NVar{\nu}}\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}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
cosh
z
𝑧
{\displaystyle{\displaystyle\cosh\NVar{z}}}
sinh
z
𝑧
{\displaystyle{\displaystyle\sinh\NVar{z}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
