Solutions of Some Nielsen-type Integrals Through Hypergeometric Technique with Applications

Abstract

Nielsen integrals and similar type of integrals were evaluated by the use of suitable contour integrals and Cauchy’s residue theorem. In this article, we obtain the solutions of Nielsen-type integrals and the associated integrals with suitable convergence conditions through hypergeometric approach using Gauss’ classical summation theorem and certain trigonometric relations. Some applications of Nielsen-type integrals are also obtained in the form of Weber-Anger type functions.