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Statements
e
-
w
w
=
2
π
∑
n
=
0
∞
(
2
n
+
1
)
𝗂
n
(
1
)
(
v
)
𝗄
n
(
u
)
P
n
(
cos
α
)
,
superscript
𝑒
𝑤
𝑤
2
𝜋
superscript
subscript
𝑛
0
2
𝑛
1
spherical-Bessel-I-1
𝑛
𝑣
spherical-Bessel-K
𝑛
𝑢
shorthand-Legendre-P-first-kind
𝑛
𝛼
{\displaystyle{\displaystyle\frac{e^{-w}}{w}=\frac{2}{\pi}\sum_{n=0}^{\infty}(%
2n+1){\mathsf{i}^{(1)}_{n}}\left(v\right)\mathsf{k}_{n}\left(u\right)P_{n}%
\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|}}
π
{\displaystyle{\displaystyle\pi}}
cos
z
𝑧
{\displaystyle{\displaystyle\cos\NVar{z}}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
i
imaginary-unit
{\displaystyle{\displaystyle\mathrm{i}}}
P
ν
(
z
)
=
P
ν
0
(
z
)
shorthand-Legendre-P-first-kind
𝜈
𝑧
Legendre-P-first-kind
0
𝜈
𝑧
{\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}%
\left(z\right)}}
𝗂
n
(
1
)
(
z
)
spherical-Bessel-I-1
𝑛
𝑧
{\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}
𝗄
n
(
z
)
spherical-Bessel-K
𝑛
𝑧
{\displaystyle{\displaystyle\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)}}
n
𝑛
{\displaystyle{\displaystyle n}}
