Analytical evaluation and asymptotic evaluation of Dawson's integral and related functions in mathematical physics

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 using the asymptotic expansion of the confluent hypergeometric function.

18 pages

References in corpus (2)

• Accurate approximations for the complex error function with small imaginary argument
• Evaluation of the non-elementary integral $\int e^{\lambda x^{\alpha }}dx,\alpha \ge 2$, and other related integrals

Cited by in corpus (4)

• Non-perturbative effects in corrections to quantum master equation arising in Bogolubov-van Hove limit
• A sampling-based approximation of the complex error function and its implementation without poles
• Abelian and non-Abelian topological behavior of a neutral spin-1/2 particle in a background magnetic field
• Analytical valuation of some non-elementary integrals involving some exponential, hyperbolic and trigonometric elementary functions and derivation of new probability measures generalizing the gamma-type and normal distributions