Open AccessOn Closed Form Expressions for Trigonometric Series and Series Involving Bessel or Struve Functions
Author(s) -
Slobodan B. Tričković,
Miomir S. Stanković,
Violeta N. Aleksis
Publication year - 2003
Publication title -
zeitschrift für analysis und ihre anwendungen
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.567
H-Index - 35
eISSN - 1661-4534
pISSN - 0232-2064
DOI - 10.4171/zaa/1139
Subject(s) - struve function , bessel function , mathematics , series (stratigraphy) , bessel polynomials , trigonometric series , trigonometric integral , riemann zeta function , riemann hypothesis , bessel process , mathematical analysis , trigonometric functions , pure mathematics , trigonometry , geometry , orthogonal polynomials , jacobi polynomials , classical orthogonal polynomials , paleontology , macdonald polynomials , biology , gegenbauer polynomials
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.
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