P A Martin 2008 J. Phys. A: Math. Theor. 41 015207 doi:10.1088/1751-8113/41/1/015207
On functions defined by sums of products of Bessel functions
P A Martin
Show affiliationsVarious functions, defined as infinite series of products of Bessel functions of the first kind, are studied. Integral representations are obtained, and then used to deduce asymptotic approximations. Although several methods have been investigated (including power series expansions and integral transforms), methods based on Fourier series emerge as the most useful.
- PACS
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02.30.Mv Approximations and expansions
- MSC
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40G10 Abel, Borel and power series methods
41A58 Series expansions (e.g. Taylor, Lidstone series, but not Fourier series)
41A60 Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (See also 30E15)
- Subjects
- Dates
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Issue 1 (11 January 2008)
Received 28 June 2007, in final form 13 November 2007
Published 12 December 2007
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On functions defined by sums of products of Bessel functions
P A Martin 2008 J. Phys. A: Math. Theor. 41 015207
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