Affiliation:
1. Katholieke Universiteit Leuven, Heverlee, Belgium
Abstract
We present an algorithm to compute integrals of the form ∫
∞
0
x
m
∏
k
i
= 1
J
ν
i
(
a
i
x
)
dx
with
J
ν
i
(
x
) the Bessel function of the first kind and (real) order ν
i
. The parameter
m
is a real number such that ∑
i
ν
i
+
m
> −1 and the coefficients
a
i
are strictly positive real numbers. The main ingredients in this algorithm are the well-known asymptotic expansion for
J
ν
i
(
x
) and the observation that the infinite part of the integral can be approximated using the incomplete Gamma function Γ(
a
,
z
). Accurate error estimates are included in the algorithm, which is implemented as a MATLAB program.
Publisher
Association for Computing Machinery (ACM)
Subject
Applied Mathematics,Software
Cited by
14 articles.
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