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Statements
S
μ
,
ν
(
z
)
=
s
μ
,
ν
(
z
)
+
2
μ
-
1
Γ
(
1
2
μ
+
1
2
ν
+
1
2
)
Γ
(
1
2
μ
-
1
2
ν
+
1
2
)
(
sin
(
1
2
(
μ
-
ν
)
π
)
J
ν
(
z
)
-
cos
(
1
2
(
μ
-
ν
)
π
)
Y
ν
(
z
)
)
,
Lommel-S
𝜇
𝜈
𝑧
Lommel-s
𝜇
𝜈
𝑧
superscript
2
𝜇
1
Euler-Gamma
1
2
𝜇
1
2
𝜈
1
2
Euler-Gamma
1
2
𝜇
1
2
𝜈
1
2
1
2
𝜇
𝜈
𝜋
Bessel-J
𝜈
𝑧
1
2
𝜇
𝜈
𝜋
Bessel-Y-Weber
𝜈
𝑧
{\displaystyle{\displaystyle S_{{\mu},{\nu}}\left(z\right)=s_{{\mu},{\nu}}%
\left(z\right)+2^{\mu-1}\Gamma\left(\tfrac{1}{2}\mu+\tfrac{1}{2}\nu+\tfrac{1}{%
2}\right)\Gamma\left(\tfrac{1}{2}\mu-\tfrac{1}{2}\nu+\tfrac{1}{2}\right)\*%
\left(\sin\left(\tfrac{1}{2}(\mu-\nu)\pi\right)\,J_{\nu}\left(z\right)-\cos%
\left(\tfrac{1}{2}(\mu-\nu)\pi\right)\,Y_{\nu}\left(z\right)\right),}}
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)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
s
μ
,
ν
(
z
)
Lommel-s
𝜇
𝜈
𝑧
{\displaystyle{\displaystyle s_{{\NVar{\mu}},{\NVar{\nu}}}\left(\NVar{z}\right%
)}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
sin
z
𝑧
{\displaystyle{\displaystyle\sin\NVar{z}}}
z
𝑧
{\displaystyle{\displaystyle z}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
