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