On the Symmetries of the q-Bernoulli Polynomials

Abstract EN

Kupershmidt and Tuenter have introduced reflection symmetries for the q-Bernoulli numbers and the Bernoulli polynomials in (2005), (2001), respectively.

However, they have not dealt with congruence properties for these numbers entirely.

Kupershmidt gave a quantization of the reflection symmetry for the classical Bernoulli polynomials.

Tuenter derived a symmetry of power sum polynomials and the classical Bernoulli numbers.

In this paper, we study the new symmetries of the q-Bernoulli numbers and polynomials, which are different from Kupershmidt's and Tuenter's results.

By using our symmetries for the q-Bernoulli polynomials, we can obtain some interesting relationships between q-Bernoulli numbers and polynomials.