Special Issue "Special Functions with Applications to Mathematical Physics III"

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematical Physics".

Deadline for manuscript submissions: 30 September 2021.

Special Issue Editor

Prof. Francesco Mainardi
E-Mail Website
Guest Editor
Department of Physics and Astronomy, University of Bologna, Via Irnerio, 46, I-40126 Bologna, Italy
Interests: special functions; fractional calculus complex analysis; asymptotic methods; diffusion and wave propagation problems
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Special Issue Information

Dear Colleagues,

This Special Issue includes theories and applications of high transcendental functions mainly included in the list of keywords:

  • Mittag–Leffler and related functions, and their applications in mathematical physics;
  • Wright and related functions and their applications in mathematical physics;
  • Exponential Integrals and their extensions with applications in mathematical physics;
  • Generalized hypergeometric functions and their extensions with applications.

However, this Special Issue is not limited to the above list, when the content of a paper is clearly related to some high transcendental functions and their applications. Special attention is reserved for the special functions exhibiting some relevance in the framework of the theories and applications of the fractional calculus and in their visualization through illuminating plots. Both research and survey pages are well accepted.

This issue is a continuation of the previous successful Special Issue “Special Functions with Applications to Mathematical Physics II”.

Prof. Francesco Mainardi
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Published Papers (2 papers)

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Review

Review
Series in Le Roy Type Functions: A Set of Results in the Complex Plane—A Survey
by
Mathematics 2021, 9(12), 1361; https://doi.org/10.3390/math9121361 (registering DOI) - 12 Jun 2021
Viewed by 130
Abstract
This study is based on a part of the results obtained in the author’s publications. An enumerable family of the Le Roy type functions is considered herein. The asymptotic formula for these special functions in the cases of `large’ values of indices, that [...] Read more.
This study is based on a part of the results obtained in the author’s publications. An enumerable family of the Le Roy type functions is considered herein. The asymptotic formula for these special functions in the cases of `large’ values of indices, that has been previously obtained, is provided. Further, series defined by means of the Le Roy type functions are considered. These series are studied in the complex plane. Their domains of convergence are given and their behaviour is investigated `near’ the boundaries of the domains of convergence. The discussed asymptotic formula is used in the proofs of the convergence theorems for the considered series. A theorem of the Cauchy–Hadamard type is provided. Results of Abel, Tauber and Littlewood type, which are analogues to the corresponding theorems for the classical power series, are also proved. At last, various interesting particular cases of the discussed special functions are considered. Full article
(This article belongs to the Special Issue Special Functions with Applications to Mathematical Physics III)
Review
The Bateman Functions Revisited after 90 Years—A Survey of Old and New Results
Mathematics 2021, 9(11), 1273; https://doi.org/10.3390/math9111273 - 01 Jun 2021
Viewed by 311
Abstract
The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is only mentioned as [...] Read more.
The Bateman functions and the allied Havelock functions were introduced as solutions of some problems in hydrodynamics about ninety years ago, but after a period of one or two decades they were practically neglected. In handbooks, the Bateman function is only mentioned as a particular case of the confluent hypergeometric function. In order to revive our knowledge on these functions, their basic properties (recurrence functional and differential relations, series, integrals and the Laplace transforms) are presented. Some new results are also included. Special attention is directed to the Bateman and Havelock functions with integer orders, to generalizations of these functions and to the Bateman-integral function known in the literature. Full article
(This article belongs to the Special Issue Special Functions with Applications to Mathematical Physics III)
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