Bicomplex Mittag-Leffler Function and Properties

TL;DR

This paper introduces a bicomplex extension of the Mittag-Leffler function, exploring its properties, convergence, and various mathematical relations to enhance its applicability in physical sciences.

Contribution

It defines the bicomplex Mittag-Leffler function and investigates its analyticity, convergence, and key properties, which were not previously established.

Findings

Established the analyticity and convergence region of the bicomplex Mittag-Leffler function.

Derived integral representations, recurrence relations, and differential formulas.

Extended the mathematical framework of Mittag-Leffler functions to bicomplex analysis.

Abstract

With the increasing importance of the Mittag-Leffler function in the physical applications, these days many researchers are studying various generalizations and extensions of the Mittag-Leffler function. In this paper efforts are made to define bicomplex extension of the Mittag-Leffler function and also its analyticity and region of convergence are discussed. Various properties of the bicomplex Mittag-Leffler function including integral representation, recurrence relations, duplication formula and differential relations are established.