A survey of some recent developments on higher transcendental functions of analytic number theory and applied mathematics
Date
2021
Authors
Srivastava, H.M.
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
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.
Description
Keywords
gamma, digamma and polygamma functions, hypergeometric functions and their generalizations and multivariate extensions, Riemann and Hurwitz (or generalized) Zeta functions, Lerch's transcendent and the Hurwitz-Lerch Zeta functions, Mittag-Leffler type functions, Fox-Wright hypergeometric function, Riemann-Liouville and related fractional derivative operators, Liouville-Caputo fractional derivative operator, Fox-Wright hypergeometric function, generalized Fox-Wright function, operators of fractional calculus, quantum or basic (or q-) analysis, fractional-order quantum or basic (or q-) analysis
Citation
Srivastava, H. M. (2021). “A survey of some recent developments on higher transcendental functions of analytic number theory and applied mathematics.” Symmetry, 13(12), 2294. https://doi.org/10.3390/sym13122294