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Statements
Io
2
m
+
1
(
z
,
h
)
=
(
-
1
)
s
∑
ℓ
=
0
∞
(
-
1
)
ℓ
A
2
ℓ
+
1
2
m
+
1
(
h
2
)
A
2
s
+
1
2
m
+
1
(
h
2
)
(
I
ℓ
-
s
(
h
e
-
z
)
I
ℓ
+
s
+
1
(
h
e
z
)
-
I
ℓ
+
s
+
1
(
h
e
-
z
)
I
ℓ
-
s
(
h
e
z
)
)
,
modified-Mathieu-Io
2
𝑚
1
𝑧
ℎ
superscript
1
𝑠
superscript
subscript
ℓ
0
superscript
1
ℓ
superscript
subscript
𝐴
2
ℓ
1
2
𝑚
1
superscript
ℎ
2
superscript
subscript
𝐴
2
𝑠
1
2
𝑚
1
superscript
ℎ
2
modified-Bessel-first-kind
ℓ
𝑠
ℎ
superscript
𝑒
𝑧
modified-Bessel-first-kind
ℓ
𝑠
1
ℎ
superscript
𝑒
𝑧
modified-Bessel-first-kind
ℓ
𝑠
1
ℎ
superscript
𝑒
𝑧
modified-Bessel-first-kind
ℓ
𝑠
ℎ
superscript
𝑒
𝑧
{\displaystyle{\displaystyle\mathrm{Io}_{2m+1}\left(z,h\right)=(-1)^{s}\sum_{%
\ell=0}^{\infty}(-1)^{\ell}\frac{A_{2\ell+1}^{2m+1}(h^{2})}{A_{2s+1}^{2m+1}(h^%
{2})}\left(I_{\ell-s}\left(he^{-z}\right)I_{\ell+s+1}\left(he^{z}\right)-I_{%
\ell+s+1}\left(he^{-z}\right)I_{\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)}}
Io
n
(
z
,
h
)
modified-Mathieu-Io
𝑛
𝑧
ℎ
{\displaystyle{\displaystyle\mathrm{Io}_{\NVar{n}}\left(\NVar{z},\NVar{h}%
\right)}}
m
𝑚
{\displaystyle{\displaystyle m}}
h
ℎ
{\displaystyle{\displaystyle h}}
z
𝑧
{\displaystyle{\displaystyle z}}
A
m
(
q
)
subscript
𝐴
𝑚
𝑞
{\displaystyle{\displaystyle A_{m}(q)}}
Identifiers
