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

By Yilmaz Simsek, Veli Kurt, Daeyeoul Kim. 2007

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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: where is the twisted (h, q)-Bernoulli polynomials. We also define new identities involving (h, q)-Bernoulli polnomials and numbers.

Subfields: Algebra and Number Theory, Applied Mathematics, Discrete Mathematics and Combinatorics

View Paper: https://www.semanticscholar.org/paper/a54bfba8c60dcf48638022a8189b9371f215e49e

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In Algebra and Number Theory

In Applied Mathematics

In Discrete Mathematics and Combinatorics

Citations in the corpus

Complete sum of products of (h, q)-extension of Euler polynomials and numbers (2010, methodology): “In [ 23 ], Simsek et al gave complete sums of products of (h,q)-Bernoulli polynomials and numbers.”
The multiplication formulas for the Apostol–Bernoulli and Apostol–Euler polynomials of higher order (2009, background): “More investigations about this subject can be found in 6 , 8–11 , 17–20 , 22 and related references.”