Abstract
Abstract. This paper deals with the study of newly deflned spe-cial function known as k -Bessel’s function due to Gehlot [2]. Cer-tain integral representations of k -Bessel’s function are investigated.Known integrals of classical Bessel’s function are seen to follow asspecial cases of our main results. 1. IntroductionBessel functions are important in studying solutions of difierentialequations, and they are associated with a wide range of problems inmany areas of mathematical physics, like problems of acoustics, radiophysics, hydrodynamics, and atomic and nuclear physics. These con-siderations have led various workers in the fleld of special functions forexploring the possible extensions and applications for the Bessel func-tion. A useful generalization of the Bessel function called as k -Besselfunction has been introduced and studied in [2]. Here we aim at pre-senting certain integral representations for the k -Bessel functions.Throughout this paper, let C ; R ; R + ; Z ; Z i ; Nbe the sets of complexnumbers, real numbers, positive real numbers, integers, negative inte-gers, positive integers respectively, and N
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