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

## TL;DR

This paper analytically evaluates Dawson's integral and related functions in mathematical physics using confluent hypergeometric functions, and derives their asymptotic expansions across the complex plane.

## Contribution

It provides a unified analytical framework for evaluating these functions and their asymptotics, enhancing understanding in mathematical physics applications.

## Key findings

- Analytical expressions for Dawson's integral and related functions in terms of confluent hypergeometric functions.
- Derived asymptotic expansions of these functions on the complex plane.
- Facilitated better numerical and theoretical analysis of these special functions.

## 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.