Giuseppe Dattoli, Paolo E. Ricci

Laguerre-Type Exponentials, and the Relevant
$L$-Circular and $L$-Hyperbolic Functions

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.