Riccati equation-based generalization of Dawson's integral function

TL;DR

This paper introduces a novel generalization of Dawson's integral function derived from a Riccati differential equation, including its MacLaurin expansion and an explicit formula for a matrix cofactor.

Contribution

It presents a new generalized Dawson's integral function based on Riccati equations and provides explicit formulas for its MacLaurin expansion and matrix cofactors.

Findings

Derived a new generalization of Dawson's integral.

Established the MacLaurin expansion for the generalized function.

Provided an explicit formula for a generic cofactor of a triangular matrix.

Abstract

A new generalization of Dawson's integral function based on the link between a Riccati nonlinear differential equation and a second-order ordinary differential equation is reported. The MacLaurin expansion of this generalized function is built up and to this end an explicit formula for a generic cofactor of a triangular matrix is deduced.