New approach to the complete sum of products of the twisted (h, q)-Bernoulli numbers and polynomials

Simsek Y., Kurt V., Kim D.

JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, vol.14, no.1, pp.44-56, 2007 (SCI-Expanded) identifier identifier


In this paper, by using q-Volkenborn integral[10], the first author[25] constructed new generating functions of the new twisted (h,q)-Bernoulli polynomials and numbers. We define higher-order twisted (h,q)-Bernoulli polynomials and numbers. Using these numbers and polynomials, we obtain new approach to the complete sums of products of twisted (h,q)-Bernoulli polynomials and numbers. p-adic q-Volkenborn integral is used to evaluate summations of the following form: