Coherent states associated with integral multi-index Mittag-Leffler functions

Abstract The purpose of this paper is to show that by using a certain type of discrete-continuous limit, a series of integral entities can be defined (Mittag-Leffler multi-index functions, associated coherent states and their properties), which are counterparts of the corresponding discrete entities. We built and examine the properties of a new aspect of generalized integral multi-index Mittag-Leffler functions and we constructed and examined the properties of coherent states associated with this new function. This approach is motivated through the fact that these functions can be connected with the coherent states of the continuous spectrum, as well as with so-called nu -function.