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Statements
𝒞
ν
(
w
)
w
ν
=
2
ν
Γ
(
ν
)
∑
k
=
0
∞
(
ν
+
k
)
𝒞
ν
+
k
(
u
)
u
ν
J
ν
+
k
(
v
)
v
ν
C
k
(
ν
)
(
cos
α
)
,
cylinder-function
𝜈
𝑤
superscript
𝑤
𝜈
superscript
2
𝜈
Euler-Gamma
𝜈
superscript
subscript
𝑘
0
𝜈
𝑘
cylinder-function
𝜈
𝑘
𝑢
superscript
𝑢
𝜈
Bessel-J
𝜈
𝑘
𝑣
superscript
𝑣
𝜈
ultraspherical-Gegenbauer-polynomial
𝜈
𝑘
𝛼
{\displaystyle{\displaystyle\frac{\mathscr{C}_{\nu}\left(w\right)}{w^{\nu}}=2^%
{\nu}\Gamma\left(\nu\right)\*\sum_{k=0}^{\infty}(\nu+k)\frac{\mathscr{C}_{\nu+%
k}\left(u\right)}{u^{\nu}}\frac{J_{\nu+k}\left(v\right)}{v^{\nu}}C^{(\nu)}_{k}%
\left(\cos\alpha\right),}}
|
v
e
±
i
α
|
<
|
u
|
𝑣
superscript
𝑒
plus-or-minus
𝑖
𝛼
𝑢
{\displaystyle{\displaystyle|ve^{\pm i\alpha}|<|u|}}
J
ν
(
z
)
Bessel-J
𝜈
𝑧
{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
Γ
(
z
)
Euler-Gamma
𝑧
{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
𝒞
ν
(
z
)
cylinder-function
𝜈
𝑧
{\displaystyle{\displaystyle\mathscr{C}_{\NVar{\nu}}\left(\NVar{z}\right)}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
C
n
(
λ
)
(
x
)
ultraspherical-Gegenbauer-polynomial
𝜆
𝑛
𝑥
{\displaystyle{\displaystyle C^{(\NVar{\lambda})}_{\NVar{n}}\left(\NVar{x}%
\right)}}
k
𝑘
{\displaystyle{\displaystyle k}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
Identifiers
