The q-Binomial Coefficient for Negative Arguments and Some q-Binomial Summation Identities
Combinatorics
2023-01-12 v4 Number Theory
Abstract
Using a property of the q-shifted factorial, an identity for q-binomial coefficients is proved, which is used to derive the formulas for the q-binomial coefficient for negative arguments. The result is in agreement with an earlier paper about the normal binomial coefficient for negative arguments. Some new q-binomial summation identities are derived, and the formulas for negative arguments transform some of these summation identities into each other. One q-binomial summation identity is transformed into a new q-binomial summation identity.
Cite
@article{arxiv.2211.08256,
title = {The q-Binomial Coefficient for Negative Arguments and Some q-Binomial Summation Identities},
author = {M. J. Kronenburg},
journal= {arXiv preprint arXiv:2211.08256},
year = {2023}
}