Construction of Degenerate $q$-Daehee Polynomials with Weight $\alpha $ and its Applications

Abstract

The fundamental aim of the present paper is to deal with introducing a new family of Daehee polynomials which is called degenerate $q$-Daehee polynomials with weight $\alpha$ by using $p$-adic $q$-integral on $\mathbb{Z}_{p}$. From this definition, we obtain some new summation formulae and properties. We also introduce the degenerate $q$-Daehee polynomials of higher order with weight $\alpha $ and obtain some new interesting identities.

Keywords

• Weighted q-Bernoulli polynomials
• Stirling numbers of first kind
• Stirling numbers of second kind
• Degenerate $q$-Daehee polynomials with weight $\alpha $

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