Explicit Formulas involving q-Euler Numbers and Polynomials

In this paper, we deal with q-Euler numbers and q-Bernoulli numbers. We derive some interesting relations for q-Euler numbers and polynomials by using their generating function and derivative operator. Also, we show between the q-Euler numbers and q-Bernoulli numbers via the p-adic q-integral in the p-adic integer ring.Comment: 9 pages, submitte

Fourier Series of the Periodic Bernoulli and Euler Functions

We give some properties of the periodic Bernoulli functions and study the Fourier series of the periodic Euler functions which are derived periodic functions from the Euler polynomials. And we derive the relations between the periodic Bernoulli functions and those from Euler polynomials by using the Fourier series

Arithmetic Identities Involving Bernoulli and Euler Numbers

The purpose of this paper is to give some arithmatic identities for the Bernoulli and Euler numbers. These identities are derived from the several p-adic integral equations on ℤp