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Statements
ε
s
Ke
2
m
(
z
,
h
)
=
∑
ℓ
=
0
∞
A
2
ℓ
2
m
(
h
2
)
A
2
s
2
m
(
h
2
)
(
I
ℓ
-
s
(
h
e
-
z
)
K
ℓ
+
s
(
h
e
z
)
+
I
ℓ
+
s
(
h
e
-
z
)
K
ℓ
-
s
(
h
e
z
)
)
,
subscript
𝜀
𝑠
modified-Mathieu-Ke
2
𝑚
𝑧
ℎ
superscript
subscript
ℓ
0
superscript
subscript
𝐴
2
ℓ
2
𝑚
superscript
ℎ
2
superscript
subscript
𝐴
2
𝑠
2
𝑚
superscript
ℎ
2
modified-Bessel-first-kind
ℓ
𝑠
ℎ
superscript
𝑒
𝑧
modified-Bessel-second-kind
ℓ
𝑠
ℎ
superscript
𝑒
𝑧
modified-Bessel-first-kind
ℓ
𝑠
ℎ
superscript
𝑒
𝑧
modified-Bessel-second-kind
ℓ
𝑠
ℎ
superscript
𝑒
𝑧
{\displaystyle{\displaystyle\varepsilon_{s}\mathrm{Ke}_{2m}\left(z,h\right)=%
\sum_{\ell=0}^{\infty}\frac{A_{2\ell}^{2m}(h^{2})}{A_{2s}^{2m}(h^{2})}\left(I_%
{\ell-s}\left(he^{-z}\right)K_{\ell+s}\left(he^{z}\right)+I_{\ell+s}\left(he^{%
-z}\right)K_{\ell-s}\left(he^{z}\right)\right),}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
K
ν
(
z
)
modified-Bessel-second-kind
𝜈
𝑧
{\displaystyle{\displaystyle K_{\NVar{\nu}}\left(\NVar{z}\right)}}
Ke
n
(
z
,
h
)
modified-Mathieu-Ke
𝑛
𝑧
ℎ
{\displaystyle{\displaystyle\mathrm{Ke}_{\NVar{n}}\left(\NVar{z},\NVar{h}%
\right)}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
z
𝑧
{\displaystyle{\displaystyle z}}
ε
s
subscript
𝜀
𝑠
{\displaystyle{\displaystyle\varepsilon_{s}}}
A
m
(
q
)
subscript
𝐴
𝑚
𝑞
{\displaystyle{\displaystyle A_{m}(q)}}
Identifiers
