Extended q-Dedekind-type Daehee-Changhee sums associated with Extended q-Euler polynomials

TL;DR

This paper introduces a p-adic q-analogue of higher order Dedekind-type sums linked to Extended q-Euler polynomials, utilizing p-adic q-integrals to explore their properties.

Contribution

It presents a novel p-adic continuous function for odd primes that connects Dedekind-type sums with Extended q-Euler polynomials via p-adic q-integrals.

Findings

Defined a new p-adic q-analogue of Dedekind-type sums

Established connections with Extended q-Euler polynomials

Provided properties of the introduced sums

Abstract

In the present paper, our goal is to introduce a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order dedekind-type sums with weight alpha related to Extended q-Euler polynomials by using p-adic q-integral in the p-adic integer ring.