Analytical and asymptotic evaluations of Dawson’s integral and related functions in mathematical physics

Abstract

Abstract Dawson’s integral and related functions in mathematical physics that include the complex error function (Faddeeva’s integral), Fried–Conte (plasma dispersion) function, Jackson function, Fresnel function and Gordeyev’s integral are analytically evaluated in terms of the confluent hypergeometric function. And hence, the asymptotic expansions of these functions on the complex plane {\mathbb{C}} are derived by using the asymptotic expansion of the confluent hypergeometric function.