A q-Analog of Dual Sequences with Applications

TL;DR

This paper develops q-analog combinatorial identities involving q-dual sequences, q-binomial coefficients, q-Stirling numbers, and q-Bernoulli numbers, expanding the theoretical framework of q-calculus.

Contribution

It introduces new combinatorial identities for q-dual sequences and related q-analogues, enhancing the understanding of their algebraic and combinatorial properties.

Findings

Derived identities for q-dual sequences and polynomials

Established new relations for q-binomial coefficients and q-Stirling numbers

Extended properties of q-Bernoulli numbers and polynomials

Abstract

In the present paper combinatorial identities involving q-dual sequences or polynomials with coefficients q-dual sequences are derived. Further, combinatorial identities for q-binomial coefficients(Gaussian coefficients), q-Stirling numbers and q-Bernoulli numbers and polynomials are deduced.