In this paper we give three methods of constructing these polynomials, extending those of Ruben [28] for the top order zonal polynomials. The first two methods yield explicit formulae for the ...

Abstract In this paper we give some interesting equation of p-adic q-integrals on ℤp. From those p-adic q-integrals, we present a systemic study of some families of extended Carlitz q-Bernoulli ...