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Statements
W
n
,
1
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u
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=
ξ
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/
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I
ν
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∑
s
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n
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A
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u
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I
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B
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I
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O
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1
u
2
n
-
1
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,
subscript
𝑊
𝑛
1
𝑢
𝜉
superscript
𝜉
1
2
modified-Bessel-first-kind
𝜈
𝑢
superscript
𝜉
1
2
superscript
subscript
𝑠
0
𝑛
1
subscript
𝐴
𝑠
𝜉
superscript
𝑢
2
𝑠
𝜉
modified-Bessel-first-kind
𝜈
1
𝑢
superscript
𝜉
1
2
superscript
subscript
𝑠
0
𝑛
2
subscript
𝐵
𝑠
𝜉
superscript
𝑢
2
𝑠
1
superscript
𝜉
1
2
modified-Bessel-first-kind
𝜈
𝑢
superscript
𝜉
1
2
Big-O
1
superscript
𝑢
2
𝑛
1
{\displaystyle{\displaystyle W_{n,1}(u,\xi)=\xi^{1/2}I_{\nu}\left(u\xi^{1/2}%
\right)\sum_{s=0}^{n-1}\frac{A_{s}(\xi)}{u^{2s}}+\xi I_{\nu+1}\left(u\xi^{1/2}%
\right)\sum_{s=0}^{n-2}\frac{B_{s}(\xi)}{u^{2s+1}}+\xi^{1/2}I_{\nu}\left(u\xi^%
{1/2}\right)O\left(\frac{1}{u^{2n-1}}\right),}}
O
(
x
)
Big-O
𝑥
{\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
I
ν
(
z
)
modified-Bessel-first-kind
𝜈
𝑧
{\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
W
n
,
j
(
u
,
ξ
)
subscript
𝑊
𝑛
𝑗
𝑢
𝜉
{\displaystyle{\displaystyle W_{n,j}(u,\xi)}}
ν
𝜈
{\displaystyle{\displaystyle\nu}}
n
𝑛
{\displaystyle{\displaystyle n}}
A
s
(
ξ
)
subscript
𝐴
𝑠
𝜉
{\displaystyle{\displaystyle A_{s}(\xi)}}
B
s
(
ξ
)
subscript
𝐵
𝑠
𝜉
{\displaystyle{\displaystyle B_{s}(\xi)}}
u
𝑢
{\displaystyle{\displaystyle u}}
Identifiers
