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Zeitschrift für Analysis und ihre Anwendungen 22 (2003), No. 1, 187--198
Copyright Heldermann Verlag 2003
On Closed Form Expressions for Trigonometric Series and Series Involving Bessel
or Struve Functions
S. B. Trickovic
University of Nis, Faculty of Civil Engineering, Dept. of Mathematics, Beogradska 14, 18000 Nis,
Serbia / Yugoslavia
M. S. Stankovic
University of Nis, Faculty of Environmental Engineering, Dept. of Mathematics, Carnojevica 10a,
18000 Nis, Serbia / Yugoslavia
V. N. Aleksic
University of Nis, Faculty of Environmental Engineering, Dept. of Mathematics, Carnojevica 10a,
18000 Nis, Serbia / Yugoslavia
We first consider a summation procedure for some trigonometric series in
terms of the Riemann zeta and related functions. In some cases these series
can be brought in closed form, which means that the infinite series are
represented by finite sums. Afterwards, we show some applications of our
results to the summation of series involving Bessel or Struve functions.
Further, relying on results from the previous sections, we obtain sums of
series involving a Bessel or Struve integral. These series are also
represented as series in terms of the Riemann zeta and related functions
of reciprocal powers and can be brought in closed form in certain cases as
well. By replacing the function appearing in a Bessel and Struve integral
with particular functions, we find sums of new series.
Keywords: Bessel and Struve functions, Riemann zeta and related functions.
MSC: 33C10, 11M06, 65B10.
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