On the Summation of Series in Terms of Bessel Functions | Zendy

Slobodan B. Tričković | Zendy; Mirjana V. Vidanović | Zendy; Miomir S. Stanković | Zendy

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On the Summation of Series in Terms of Bessel Functions

Author(s) -

Slobodan B. Tričković,

Mirjana V. Vidanović,

Miomir S. Stanković

Publication year - 2006

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/1296

Subject(s) - bessel function , series (stratigraphy) , mathematics , divergent series , mathematical analysis , bessel polynomials , summation by parts , geology , orthogonal polynomials , paleontology , macdonald polynomials , difference polynomials

In this article we deal with summation formulas for the series ∑ ∞ n=1 Jμ(nx) nν , referring partly to some results from our paper in J. Math. Anal. Appl. 247 (2000) 15 – 26. We show how these formulas arise from different representations of Bessel functions. In other words, we first apply Poisson’s or Bessel’s integral, then in the sequel we define a function by means of the power series representation of Bessel functions and make use of Poisson’s formula. Also, closed form cases as well as those when it is necessary to take the limit have been thoroughly analyzed.

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