On one-sided series of Bessel functions of the first kind: ${\sum }_{m=0}^{\infty }(\pm 1{)}^m{J}_{Nm+p}(x)$

Abstract

We present generic expressions for one-sided series of Bessel functions of the first kind: ${\sum }_{m=0}^{\infty }{J}_{Nm+p}(x)$ and ${\sum }_{m=0}^{\infty }(-1{)}^m{J}_{Nm+p}(x)$. The result is expressed in terms of incomplete Lipschitz-Hankel integrals of Bessel functions of the first kind, which can be represented as Kampé de Fériet functions.

17 pages