On integrals of Bessel functions related to Weber's second exponential integral |
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| Authors: | M J Offerhaus |
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| Institution: | (1) FOM-Institute for Atomic and Molecular Physics, Amsterdam, The Netherlands |
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| Abstract: | Two closely related integrals of Bessel functions are discussed:
![$$\int\limits_0^\infty {t^{1 - 2m} e^{ - {{t^2 } \mathord{\left/ {\vphantom {{t^2 } {2z}}} \right. \kern-\nulldelimiterspace} {2z}}} J_n (t)]^2 } dt;\int\limits_0^z {u^{ - l} e^{ - u} I_n (u)} du.$$](/content/m64236p023025837/10494_2005_Article_BF01897864_TeX2GIFIE1.gif)
Whenn, m, l are integers (m andl=1,2, ...,n), both integrals can be written as closed expressions in modified Bessel functionsI
k
(z). The results are interpreted in terms of hypergeometric seriesp
F
q. Series expansions inz and in 1/z are given. |
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| Keywords: | |
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