**Giuseppe Dattoli, Paolo E. Ricci**

## Laguerre-Type Exponentials,
and the Relevant

$L$-Circular and $L$-Hyperbolic Functions

**abstract:**

Some classes of entire functions which are eigenfunctions of generalizations of
the Laguerre derivative operator are considered.

Since this property is an analog of the one characterizing the exponential
function, we refer to such functions as Laguerre-type exponentials, or shortly
$L$-exponentials. The definition of $L$-circular and $L$-hyperbolic functions
easily follows.

Applications in the framework of generalized evolution problems are also
mentioned.