An esoteric identity with many parameters and other elliptic extensions of elementary identities
Number Theory
2023-11-01 v1 Classical Analysis and ODEs
Combinatorics
Abstract
We provide elliptic extensions of elementary identities such as the sum of the first odd or even numbers, the geometric sum and the sum of the first cubes. Many such identities, and their -analogues, are indefinite sums, and can be obtained from telescoping. So we used telescoping in our study to find elliptic extensions of these identities. In the course of our study, we obtained an identity with many parameters, which appears to be new even in the -case. In addition, we recover some -identities due to Warnaar.
Keywords
Cite
@article{arxiv.2310.20219,
title = {An esoteric identity with many parameters and other elliptic extensions of elementary identities},
author = {Gaurav Bhatnagar and Archna Kumari and Michael J. Schlosser},
journal= {arXiv preprint arXiv:2310.20219},
year = {2023}
}
Comments
15 pages, comments welcome