Dipartimento di Schienze Fisiche ed Astronomiche,

Universita di Palermo,

Via Archirafi 36,

I-90123 Palermo,

ITALY

E-mail: messina@fisica.unipa.it

**Riccati equation-based generalization of the Dawson
integral function**

**Abstract:**

An interesting representation of the general integral of a linear homogeneous
second order ordinary differential equation is constructed exploiting its
link with the theory of Riccati equation. As an application we are able
to propose a new generalization of the Dawson integral function and to
find its Taylor expansion in *R*. Other novel functions are introduced
and studied by this method.