Some q-Identities derived by the ordinary derivative operator
Combinatorics
2023-08-15 v1
Abstract
In this paper, we investigate applications of the ordinary derivative operator, instead of the -derivative operator, to the theory of -series. As main results, many new summation and transformation formulas are established which are closely related to some well-known formulas such as the -binomial theorem, Ramanujan's formula, the quintuple product identity, Gasper's -Clausen product formula, and Rogers' formula, etc. Among these results is a finite form of the Rogers-Ramanujan identity and a short way to Eisenstein's theorem on Lambert series.
Cite
@article{arxiv.2308.06800,
title = {Some q-Identities derived by the ordinary derivative operator},
author = {Jin Wang and Ruiqi Ruan and Xinrong Ma},
journal= {arXiv preprint arXiv:2308.06800},
year = {2023}
}
Comments
22 pages