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Mathematics
Special Issues
Recent Advances on Ramanujan Theories in Mathematics and Physics
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Recent Advances on Ramanujan Theories in Mathematics and Physics

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 3741

Special Issue Editor

Dr. Nikolaos Bagis

E-Mail Website
Guest Editor
Department of Informatics, Aristotle University Thessaloniki, Thessaloniki, Greece
Interests: sampling theory; non-trigonometric sampling; harmonic analysis; wavelets; number theory; analytic number theory; ramanujan; ramanujan theories; elliptic functions and integrals; approximation of constants; algebricity; algebraic functions; modular equations; theta functions; quadratic and higher forms; modular functions; mock theta functions; continued fractions; inversion theory problems; complex analysis; differential equations' differential geometry; mathematical physics

Special Issue Information

Dear Colleagues,

The work of Indian mathematician Srinivasa Ramanujan profoundly influenced the current field of mathematics. Moreover, it not only influenced this science and its scientists, but also predicted physical natural phenomena that we are just beginning to understand, demonstrating his ingenuity and depth of thought.

For this Special Issue we seek high-quality papers that present original research in all fields of mathematical and physical sciences influenced by and bearing the name of Ramanujan.

Dr. Nikolaos Bagis
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 submissions that pass pre-check are 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 2600 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.

Keywords

  • Ramanujan
  • Ramanujan theories
  • elliptic functions
  • approximation of constants
  • continued fractions
  • theta functions
  • mock theta functions
  • modular forms
  • modular equations
  • number theory
  • algebraic equations
  • inversion problem theories
  • mathematical physics
  • string theory
  • theory of black holes
  • signal processing

Published Papers (2 papers)

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Research

14 pages, 307 KiB  
Article
Evaluation of Infinite Series by Integrals
by Chunli Li and Wenchang Chu
Mathematics 2022, 10(14), 2444; https://doi.org/10.3390/math10142444 - 13 Jul 2022
Cited by 2 | Viewed by 1078
Abstract
We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms. Numerous explicit formulae are [...] Read more.
We examine a large class of infinite triple series and establish a general summation formula. This is done by expressing the triple series in terms of definite integrals involving arctangent function that are evaluated in turn in closed forms. Numerous explicit formulae are tabulated for the triple series whose values result in elegant expressions as π, ln2 and the Catalan constant G. Full article
(This article belongs to the Special Issue Recent Advances on Ramanujan Theories in Mathematics and Physics)
15 pages, 367 KiB  
Article
Revisiting the Formula for the Ramanujan Constant of a Series
by Jocemar Q. Chagas, José A. Tenreiro Machado and António M. Lopes
Mathematics 2022, 10(9), 1539; https://doi.org/10.3390/math10091539 - 4 May 2022
Cited by 2 | Viewed by 1632
Abstract
The main contribution of this paper is to propose a closed expression for the Ramanujan constant of alternating series, based on the Euler–Boole summation formula. Such an expression is not present in the literature. We also highlight the only choice for the parameter [...] Read more.
The main contribution of this paper is to propose a closed expression for the Ramanujan constant of alternating series, based on the Euler–Boole summation formula. Such an expression is not present in the literature. We also highlight the only choice for the parameter a in the formula proposed by Hardy for a series of positive terms, so the value obtained as the Ramanujan constant agrees with other summation methods for divergent series. Additionally, we derive the closed-formula for the Ramanujan constant of a series with the parameter chosen, under a natural interpretation of the integral term in the Euler–Maclaurin summation formula. Finally, we present several examples of the Ramanujan constant of divergent series. Full article
(This article belongs to the Special Issue Recent Advances on Ramanujan Theories in Mathematics and Physics)
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