What type of study is this?

This is a Quantitative Study study.

October 10, 2025Open Access

Formal Calculation of Q-Binomial

Key Points

This article reveals three interrelated forms of q-binomial nested sums, enhancing q-analysis methods.
It computes formulas involving q-Eulerian numbers and polynomials, generating new results in combinatorial mathematics.
The approach connects nested sums with binomial coefficients through limits, contributing to the existing body of work.
Utilization of these formulas may enable the generalization of many classic conclusions in a straightforward manner.

Abstract

This article offers formulas for computing various q-binomial nested sums, give three forms of results, reveals the three forms of q-binomial and their interrelationships. It is a powerful tool for q-analysis, which can prove and generalize many classic conclusions in a simple way. This article also utilized it to obtain a large number of new results, including formulas for q-Eulerian numbers and polynomials. By taking the limit of q to 1, it can calculate general nested sums and analyze binomial coefficients.

Read Full Paperexternally

Perguntar à IA

Bookmark

View Full Paper

Cite This Study

Peng Ji (Wed,) studied this question.

synapsesocial.com/papers/68e861907ef2f04ca37e3f8d https://doi.org/https://doi.org/10.20944/preprints202505.0208.v2