From Bessel to Multi-Index MittagLeffler Functions

Enumerable Families, Series in them and Convergence

Bessel and Mittag–Leffler functions are prominent within mathematical and scientific fields due to increasing interest in non-conventional models within applied mathematics. Since the analytical solutions of many differential and integral equations of arbitrary order can be written as series of special functions of fractional calculus, they are now unavoidable tools for handling various mathematical models of integer or fractional order. From Bessel to Multi-Index Mittag–Leffler Functions analyzes this through the study of enumerable families of different classes of special functions.

Enumerable families are considered and the convergence of series is investigated. Providing a unified approach to the classical power series, analogues of the classical results for the power series are obtained, and the conclusion is that each of the considered series has a similar convergence behavior to a power series. Also studied are various properties of the Bessel and Mittag–Leffler functions and their generalizations, including estimations, asymptotic formulae, fractional differentiation and integration operators.

Contents:

• Preface
• Acknowledgments
• Introduction
• Bessel and Associated Functions
• Generating Functions of Bessel and Associated Bessel Functions
• Convergence of Series in Bessel Functions
• Bessel and Neumann Expansions
• The Completeness of Systems of Bessel and Associated Bessel Functions in Spaces of Holomorphic Functions
• Multi-Index Bessel Functions
• Mittag–Leffler Type Functions
• Latest Generalizations of Both the Bessel and Mittag–Leffler Type Functions
• Series in Mittag–Leffler Type Functions
• Bibliography
• Index

Readership: Pure and applied mathematicians, applied scientists in other natural sciences and engineering. Perfect for those interested in problems related to analytical solutions of various differential and integrated equations of arbitrary order modelling real processes.