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Statements
∫
0
1
2
π
Y
2
ν
(
2
z
cos
θ
)
cos
(
2
μ
θ
)
d
θ
=
1
2
π
cot
(
2
ν
π
)
J
ν
+
μ
(
z
)
J
ν
-
μ
(
z
)
-
1
2
π
csc
(
2
ν
π
)
J
μ
-
ν
(
z
)
J
-
μ
-
ν
(
z
)
,
superscript
subscript
0
1
2
𝜋
Bessel-Y-Weber
2
𝜈
2
𝑧
𝜃
2
𝜇
𝜃
𝜃
1
2
𝜋
2
𝜈
𝜋
Bessel-J
𝜈
𝜇
𝑧
Bessel-J
𝜈
𝜇
𝑧
1
2
𝜋
2
𝜈
𝜋
Bessel-J
𝜇
𝜈
𝑧
Bessel-J
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}Y_{2\nu}\left(2z\cos%
\theta\right)\cos\left(2\mu\theta\right)\mathrm{d}\theta=\tfrac{1}{2}\pi\cot%
\left(2\nu\pi\right)J_{\nu+\mu}\left(z\right)J_{\nu-\mu}\left(z\right)-\tfrac{%
1}{2}\pi\csc\left(2\nu\pi\right)J_{\mu-\nu}\left(z\right)J_{-\mu-\nu}\left(z%
\right),}}
-
1
2
<
ℜ
ν
<
1
2
1
2
𝜈
1
2
{\displaystyle{\displaystyle-\tfrac{1}{2}<\Re\nu<\tfrac{1}{2}}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
Y
ν
(
z
)
Bessel-Y-Weber
𝜈
𝑧
{\displaystyle{\displaystyle Y_{\NVar{\nu}}\left(\NVar{z}\right)}}
π
{\displaystyle{\displaystyle\pi}}
csc
z
𝑧
{\displaystyle{\displaystyle\csc\NVar{z}}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
cot
z
𝑧
{\displaystyle{\displaystyle\cot\NVar{z}}}
d
x
𝑥
{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
∫
{\displaystyle{\displaystyle\int}}
ℜ
absent
{\displaystyle{\displaystyle\Re}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
