Congruences for Generalized -Bernoulli Polynomials

Mehmet Cenkci,Veli Kurt

doi:10.1155/2008/270713

Abstract

In this paper, we give some further properties of -adic - -function of two variables, which is recently constructed by Kim (2005) and Cenkci (2006). One of the applications of these properties yields general classes of congruences for generalized -Bernoulli polynomials, which are -extensions of the classes for generalized Bernoulli numbers and polynomials given by Fox (2000), Gunaratne (1995), and Young (1999, 2001).

Highlights

Introduction and primary conceptsFor n ∈ Z, n ≥ 0, Bernoulli numbers Bn originally arise in the study of finite sums of a given power of consecutive integers
They are given by B0 1, B1 −1/2, B2 1/6, B3 0, B4 −1/30, . . ., with B2n 1 0 for odd n > 1, and
The Bernoulli polynomials Bn z can be expressed in the form zn n m0 n m

Summary

Recommended by Andrea Laforgia

We give some further properties of p-adic q-L-function of two variables, which is recently constructed by Kim 2005 and Cenkci 2006. One of the applications of these properties yields general classes of congruences for generalized q-Bernoulli polynomials, which are qextensions of the classes for generalized Bernoulli numbers and polynomials given by Fox 2000 , Gunaratne 1995 , and Young 1999, 2001.

Introduction and primary concepts

Bn z

Let D denote the region

Bn n

Note that

The binomial coefficient operator