On a degenerate q-Euler polynomials and numbers with weight

Abstract

In this paper, we define the p-adic q-integral on Z p with weight which is a generalization of Kim's definition in [T. Kim, Russ. J. Math. Phys., 9 (2002), 288-299], and derive some new and interesting identities related to degenerate q-Euler polynomials with weight and some special functions.

Applications of degenerate q-Euler and q-Changhee polynomials with weight α

“…q-analogs also appear in the study of quantum groups, matrices, identities, dynamical systems, fractals, modular groups, designs, systems, oscillators etc. [1,3,9,14,16].…”

“…In [16], for any parameters α and β, the degenerate q-Euler polynomials with weight α are defined by the generating function to be [2]…”

“…When x = 0, Ch n,q = Ch n,q (0) are called q-Changhee numbers and when q = 1, Ch n = Ch n,1 (0). In [16], the generating function of q-Changhee polynomials of the second kind with weight α, denoted by…”

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

“…Therefore, in recent years, p-adic integral and its various generalizations have been considered and extensively studied by many mathematicians, cf. [3], [4], [5], [7], [11], [12], [16], [20], [21], [22], [29].…”

“…Motivated by the works of [3], [4] and [12], we consider the degenerate q-Daehee polynomials with weight α as follows:…”