A Survey of Some Recent Developments on Higher Transcendental Functions of Analytic Number Theory and Applied Mathematics

Often referred to as special functions or mathematical functions, the origin of many members of the remarkably vast family of higher transcendental functions can be traced back to such widespread areas as (for example) mathematical physics, analytic number theory and applied mathematical sciences. H...

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Vydáno v:Symmetry (Basel) Ročník 13; číslo 12; s. 2294
Hlavní autor: Srivastava, Hari Mohan
Médium: Journal Article
Jazyk:angličtina
Vydáno: Basel MDPI AG 01.12.2021
Témata:
Applications of mathematics
Applied mathematics
Fractional calculus
Mathematical analysis
Mathematicians
Number theory
Operators (mathematics)
Parameters
Partial differential equations
Textbooks
Transcendental functions
Variables
ISSN:2073-8994, 2073-8994
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Shrnutí:Often referred to as special functions or mathematical functions, the origin of many members of the remarkably vast family of higher transcendental functions can be traced back to such widespread areas as (for example) mathematical physics, analytic number theory and applied mathematical sciences. Here, in this survey-cum-expository review article, we aim at presenting a brief introductory overview and survey of some of the recent developments in the theory of several extensively studied higher transcendental functions and their potential applications. For further reading and researching by those who are interested in pursuing this subject, we have chosen to provide references to various useful monographs and textbooks on the theory and applications of higher transcendental functions. Some operators of fractional calculus, which are associated with higher transcendental functions, together with their applications, have also been considered. Many of the higher transcendental functions, especially those of the hypergeometric type, which we have investigated in this survey-cum-expository review article, are known to display a kind of symmetry in the sense that they remain invariant when the order of the numerator parameters or when the order of the denominator parameters is arbitrarily changed.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym13122294