A note on Boole polynomials with q-parameter

TL;DR

This paper introduces a q-parameter extension of Boole polynomials using fermionic p-adic integrals, providing new identities and expanding their mathematical framework within p-adic analysis.

Contribution

It presents a novel q-extension of Boole polynomials and derives new identities, enhancing understanding of their properties in p-adic contexts.

Findings

Derived new identities for q-extended Boole polynomials

Connected Boole polynomials with fermionic p-adic integrals

Expanded the theoretical framework of Boole polynomials in p-adic analysis

Abstract

Recently, Boole polynomials have been studied by Kim and Kim over the p-adic number field. In this paper, we consider a q-extension of Boole polynomials by using the fermionic p-adic integrals on Zp and give some new identities related to those polynomials.