Explicit Formulas Involving q-Euler Numbers and Polynomials

الملخص EN

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 derive relations between the q-Euler numbers and q-Bernoulli numbers via the p-adic q-integral in the p-adic integer ring.