NOVEL IDENTITIES OF SYMMETRY FOR CARLITZ'S TWISTED $q$-BERNOULLI POLYNOMIALS UNDER $S_{4}$

IDENTITIES OF SYMMETRY FOR THE HIGHER ORDER q-BERNOULLI POLYNOMIALS

Abstract. The study of the identities of symmetry for the Bernoulli polynomials arises from the study of Gauss’s multiplication formula for the gamma function. There are many works in this direction. In the sense of p-adic analysis, the q-Bernoulli polynomials are natural extensions of the Bernoulli and Apostol-Bernoulli polynomials (see the introduction of this paper). By using the N-fold iter...

Some identities of symmetry for the degenerate q-Bernoulli polynomials under symmetry group of degree n

Recently, Kim-Kim Introduced some interesting identities of symmetry for qBernoulli polynomials under symmetry group of degree n. In this paper, we study the degenerate q-Euler polynomials and derive some identities of symmetry for these polynomials arising from the p-adic q-integral on Zp. AMS subject classification: 11B68, 11S80, 05A19, 05A30.

New symmetric identities of Carlitz’s generalized twisted q-Bernoulli polynomials under S3

In this paper, the authors consider the Carlitz’s generalized twisted q-Bernoulli polynomials attached to χ and investigate some novel symmetric identities for these polynomials arising from the p-adic q-integral on Zp under S3.

Identities of Symmetry for Carlitz q-Bernoulli Polynomials Arising from q-Volkenborn Integrals on Zp under Symmetry Group S3

Identities of Symmetry for q-Euler Polynomials

In this paper, we derive eight basic identities of symmetry in three variables related to q-Euler polynomials and the q -analogue of alternating power sums. These and most of their corollaries are new, since there have been results only about identities of symmetry in two variables. These abundance of symmetries shed new light even on the existing identities so as to yield some further interest...