On applications for Mahler expansion associated with p-adic q-integrals

Abstract

In this paper, we primarily consider a generalization of the fermionic p-adic q-integral on p including the parameters ? and ? and investigate its some basic properties. By means of the foregoing integral, we introduce two generalizations of q-Changhee polynomials and numbers as q-Changhee polynomials and numbers with weight (??) and q-Changhee polynomials and numbers of second kind with weight (??). For the mentioned polynomials, we obtain new and interesting relationships and identities including symmetric relation, recurrence relations and correlations associated with the weighted q-Euler polynomials, Q-Stirling numbers of the second kind and Stirling numbers of first and second kinds. Then, we discover multifarious relationships among the two types of weighted q-Changhee polynomials and p-adic gamma function. Also, we compute the weighted fermionic p-adic q-integral of the derivative of p-adic gamma function. Moreover, we give a novel representation for the p-adic Euler constant by means of the weighted q-Changhee polynomials and numbers. We finally provide a quirky explicit formula for p-adic Euler constant. © 2019 World Scientific Publishing Company.