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

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Simsek Y., Kurt V., Kim D.

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

• Publication Type: Article / Article
• Volume: 14 Issue: 1
• Publication Date: 2007
• Doi Number: 10.2991/jnmp.2007.14.1.5
• Journal Name: JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Page Numbers: pp.44-56
• Akdeniz University Affiliated: Yes

Abstract

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: