Bicomplex Mittag-Leffler function and associated properties

Volume 15, Issue 1, pp 48--60 http://dx.doi.org/10.22436/jnsa.015.01.04

Publication Date: July 03, 2021 Submission Date: March 24, 2021 Revision Date: May 02, 2021 Accteptance Date: May 28, 2021

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Authors

R. Agarwal - Department of Mathematics, Malaviya National Institute of Technology, Jaipur-302017, India. U. P. Sharma - Department of Mathematics, Malaviya National Institute of Technology, Jaipur-302017, , India. R. P. Agarwal - Department of Mathematics, Texas A\(\&\)M University, Kingsville 700 University Blvd., Kingsville, USA.

Abstract

With the increasing importance of the Mittag-Leffler function in 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 the 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.

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Keywords

• Bicomplex numbers
• exponential function
• Gamma function
• Mittag-Leffler function

MSC

•  30G35
•  33E12

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