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DLMF:10.66#Ex2
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Formula:4542
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MaRDI QID
Q4542
Label: DLMF:10.66#Ex2
Digital Library of Mathematical Functions ID
10.66#Ex2
bei
n
(
x
2
)
=
∑
k
=
-
∞
∞
(
-
1
)
n
+
k
J
n
+
2
k
+
1
(
x
)
I
2
k
+
1
(
x
)
.
Kelvin-bei
𝑛
𝑥
2
superscript
subscript
𝑘
superscript
1
𝑛
𝑘
Bessel-J
𝑛
2
𝑘
1
𝑥
modified-Bessel-first-kind
2
𝑘
1
𝑥
{\displaystyle{\displaystyle\operatorname{bei}_{n}\left(x\sqrt{2}\right)=\sum_% {k=-\infty}^{\infty}(-1)^{n+k}J_{n+2k+1}\left(x\right)I_{2k+1}\left(x\right).}}
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