Authors: Stanković, Miomir 
Vidanović, Mirjana
Tričković, Slobodan
Title: Some series over the product of two trigonometric functions and series involving bessel functions
Journal: Zeitschrift fur Analysis und ihre Anwendung
Volume: 20
Issue: 1
First page: 335
Last page: 346
Issue Date: 1-Dec-2001
ISSN: 0232-2064
DOI: 10.1080/10652460108819318
Abstract: 
The sum of the series Sα = Sα (s, a, b, f(y), g(x)) = Σn=1∞ (s)n-1 f((an - b)y) g((an - b)x)/(an - b)α involving the product of two trigonometric functions is obtained using the sum of the series Σn=1∞ (s)(n-1) f((an - b)x)/(an - b)α = cπ/2(α)f(πα/2) xα-1 + Σi=0∞(-1)i f(α - 2i - δ)/(2i + δ)! x2i+δ whose terms involve one trigonometric function. The first series is represented as series in terms of the Riemann zeta and related functions, which has a closed form in certain cases. Some applications of these results to the summation of series containing Bessel functions are given. The obtained results also include as special cases formulas in some known books. We further show how to make use of these results to obtain closed form solutions of some boundary value problems in mathematical physics. © Heldermann Verlag.
Keywords: Bessel functions | Riemann zeta and related functions
Publisher: Taylor & Francis

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