On the summation of series in terms of Bessel functions
This article deals with summation formulas for the series \[ \sum^\infty_{n=1} {J_\mu(nx)\over n^\nu}\tag{1} \] referring partly to some results from other paper of the same authors in [J. Math. Anal. Appl. 247, No. 1, 15--26 (2000; Zbl 0957.33003)]. At first the authors show how different summation formulas for the series (1) arise from integral representations of Bessel functions, Poisson's and Bessel's integral. Another representation of Bessel functions is considered and defined a suitable function to apply Poisson's formula and find one more summation formula for (1). It can be interesting for the rational approximation. See \textit{N. Hayek Calil}, \textit{P. González-Vera} and \textit{F. Pérez-Acosta} [Numer. Algorithms 3, No. 1--4, 235--244 (1992; Zbl 0784.65011)].
scientific article; zbMATH DE number 5073451