A generalized computation procedure for Ramanujan-type identities and cubic Shevelev sum

Peter J.-S. Shiue, Anthony G. Shannon, Shen C. Huang, Jorge E. Reyes
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 29, 2023, Number 1, Pages 98–129
DOI: 10.7546/nntdm.2023.29.1.98-129
Full paper (PDF, 388 Kb)

Details

Authors and affiliations

Peter J.-S. Shiue
Department of Mathematical Sciences, University of Nevada, Las Vegas
Las Vegas, NV, 89154, United States of America

Anthony G. Shannon
Warrane College, University of New South Wales
Kensington, NSW 2033, Australia

Shen C. Huang
Department of Mathematical Sciences, University of Nevada, Las Vegas
Las Vegas, NV, 89154, United States of America

Jorge E. Reyes
Department of Mathematical Sciences, University of Nevada, Las Vegas
Las Vegas, NV, 89154, United States of America

Abstract

A generalized Computation procedure for construction of the Ramanujan-type from a given general cubic equation and a cosine Ramanujan-type identity is developed from detailed analyses of the properties of Ramanujan-type cubic equations. Examples are provided together with cubic Shevelev sums.

Keywords

• Ramanujan cubic polynomials
• Ramanujan cubic polynomials of the second kind
• Cubic Shevelev sum

2020 Mathematics Subject Classification

• 11C08
• 11D25
• 11Y99

References

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Manuscript history

• Received: 25 December 2022
• Revised: 28 February 2023
• Accepted: 2 March 2023
• Online First: 6 March 2023

Copyright information

Ⓒ 2023 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).