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Statements
(
ber
′
x
)
2
+
(
bei
′
x
)
2
∼
e
x
2
2
π
x
(
1
-
3
4
2
1
x
+
9
64
1
x
2
+
75
256
2
1
x
3
+
2475
8192
1
x
4
+
⋯
)
.
asymptotic-expansion
superscript
diffop
Kelvin-ber
1
𝑥
2
superscript
diffop
Kelvin-bei
1
𝑥
2
superscript
𝑒
𝑥
2
2
𝜋
𝑥
1
3
4
2
1
𝑥
9
64
1
superscript
𝑥
2
75
256
2
1
superscript
𝑥
3
2475
8192
1
superscript
𝑥
4
⋯
{\displaystyle{\displaystyle\left(\operatorname{ber}'x\right)^{2}+\left(%
\operatorname{bei}'x\right)^{2}\sim\frac{e^{x\sqrt{2}}}{2\pi x}\left(1-\frac{3%
}{4\sqrt{2}}\frac{1}{x}+\frac{9}{64}\frac{1}{x^{2}}+\frac{75}{256\sqrt{2}}%
\frac{1}{x^{3}}+\frac{2475}{8192}\frac{1}{x^{4}}+\cdots\right).}}
bei
ν
(
x
)
Kelvin-bei
𝜈
𝑥
{\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
ber
ν
(
x
)
Kelvin-ber
𝜈
𝑥
{\displaystyle{\displaystyle\operatorname{ber}_{\NVar{\nu}}\left(\NVar{x}%
\right)}}
∼
asymptotic-expansion
{\displaystyle{\displaystyle\sim}}
π
{\displaystyle{\displaystyle\pi}}
e
{\displaystyle{\displaystyle\mathrm{e}}}
x
𝑥
{\displaystyle{\displaystyle x}}
Identifiers
