In this paper we focus on r-geometric polynomials, r-exponential polynomials and their harmonic versions. We show that harmonic versions of these polynomials and their generalizations are useful for obtaining closed forms of some series related to harmonic numbers.

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:

In this paper, we study on two subjects. We first construct degenerate analogues of Dedekind sums in the sense of Apostol, Carlitz and Takács, and prove the corresponding reciprocity formulas. Secondly, we define generalized Dedekind character sums, which are explicit extensions of Berndt's definition, and prove the reciprocity laws. From the derived reciprocity laws, we obtain Berndt's reciprocity laws as special cases.

The aim of this paper is to study generating function of the Hermite-Kampė de Fėriet based second kind Genocchi polynomials. We also give some identities related to these polynomials.

No abstract