Integral transforms and summation of some Schlömilch series

Authors

  • Slobodan B. Tričković University of Niš, Faculty of Civil Engineering, Dept. of Mathematics, Beogradska 14, 18000 Niš, Serbia Author
  • Miomir S. Stanković University of Niš, Faculty of Environmental Engineering, Dept. of Mathematics, Čarnojevića 10a, 18000 Niš, Serbia Author
  • Mirjana V. Vidanović University of Niš, Faculty of Environmental Engineering, Dept. of Mathematics, Čarnojevića 10a, 18000 Niš, Serbia Author
  • Violeta N. Aleksić University of Niš, Faculty of Environmental Engineering, Dept. of Mathematics, Čarnojevića 10a, 18000 Niš, Serbia Author

Keywords:

Bessel functions, the Riemann zeta and related functions

Subjects:

33C10, 11M06, 65B10

Abstract

In this paper we present a survey of the results given in the papers [11, 12, 13, 14]. Connections between integral transforms and some Schlömilch series have also been considered. These series are represented in terms of the Riemann zeta and related functions of reciprocal powers and can be brought in so called closed form in certain cases, which means that the infinite series are represented by finite sums. As applications of our results, recursive relations of some related functions and the sums of new Schlömilch series involving the Neumann, MacDonald, Struve or Bessel functions are given as well.

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Published

2002-10-15

Issue

Vol. 54 No. 3–4 (2002): Vol. 54, Issue 3–4

Section

Articles

License

Copyright (c) 2002 Authors retain copyright to their work.

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.