This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In this paper, we investigate some symmetric properties of p-adic q-integral on Z p. A question was asked in [10] as to finding formulae of symmetries for the generalized Ca...

* Correspondence: [email protected] Department of Mathematics, KAIST, 373-1 Guseong-dong, Yuseong-gu, Daejeon 305-701, South Korea Full list of author information is available at the end of the article Abstract The q-analogues of many well known formulas are derived by using several results of q-Bernoulli, q-Euler numbers and polynomials. The q-analogues of ζ-type functions are given by usi...

The Cauchy-type product of two arithmetic functions f and g on nonnegative integers is defined by (f • g)(k) := ∑k m=0 ( k m ) f(m)g(k −m). We explore some algebraic properties of the aforementioned convolution, which is a fundamental characteristic of the identities involving the Bernoulli numbers, the Bernoulli polynomials, the power sums, the sums of products, and so forth.

In our recent paper with Srivastava [D. Cvijović, H.M. Srivastava, Summation of a family of finite secant sums, Appl. Math. Comput. 190 (2007) 590–598] a remarkably general family of the finite secant sums was summed in closed form by choosing a particularly convenient integration contour and making use of the calculus of residues. In this sequel, we show that this procedure can be extended and...

The Sheffer polynomials and the monomiality principle, along with the underlying operational formalism, offer a powerful tool for investigation of the properties of a wide class of polynomials. We present, within such a context, a self-contained theory of such familiar systems of polynomials as the Euler, Bernoulli, Bessel and other clasical polynomials and show how the derivation of some of th...