Riccati equation-based generalization of Dawson's integral function

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.

11 pages. Accepted on Mathematical Methods in the Applied Sciences