On the numerical evaluation of an oscillating infinite series II

Abstract

An oscillating infinite series involving products of Bessel function J 0(x) was evaluated and computed numerically in [1]. In this paper, an oscillating infinite series involving trigonometric function sin(x), is also transformed first into the sum of three infinite integrals by using contour integration and then the infinite integral with oscillating integrand is transformed through some identities into an expression containing modified Bessel function K 1(x). This expression and the other infinite integrals are evaluated numerically without encountering any computational difficulties.