Identities of symmetry for q-Bernoulli polynomials

In this paper, we derive eight basic identities of symmetry in three variables related to $q$-Bernoulli polynomials and the $q$-analogue of 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 interesting ones. The derivations of identities are based on the $p$-adic integral expression of the generating function for the $q$-Bernoulli polynomials and the quotient of integrals that can be expressed as the exponential generating function for the $q$-analogue of power sums.Comment: No comment

A Note on Three Variable Symmetric Identities for Modified q-Bernoulli Polynomials Arising from Bosonic p-Adic Integral on Z p

Abstract Recently, Dolgy-Kim-Kim derived some identities of Carlitz's q-Bernoulli polynomials under symmetry group S 3 ([5]). In this paper, we investigate identities of 4576 Dmitry V. Dolgy, Taekyun Kim, Feng Qi and Jong Jin Seo symmetry for the modified Carlitz's q-Bernoulli polynomials which are different the symmetric identities of Dolgy-Kim-Kim for the Carlitz's q-Bernoulli polynomials

Expansion formulas for Apostol type qq-Appell polynomials, and their special cases

We present identities of various kinds for generalized $q$-Apostol-Bernoulli and Apostol-Euler polynomials and power sums, which resemble $q$-analogues of formulas from the 2009 paper by Liu and Wang. These formulas are divided into two types: formulas with only $q$-Apostol-Bernoulli, and only $q$-Apostol-Euler polynomials, or so-called mixed formulas, which contain polynomials of both kinds.This can be seen as a logical consequence of the fact that the $q$-Appell polynomials form a commutative ring. The functional equations for Ward numbers operating on the $q$-exponential function, as well as symmetry arguments, are essential for many of the proofs.We conclude by finding multiplication formulas for two $q$-Appell polynomials of general form. This brings us to the $q$-H polynomials, which were discussed in a previous paper

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 interesting ones. The derivations of identities are based on the $p$-adic integral expression of the generating function for the $q$-Euler polynomials and the quotient of integrals that can be expressed as the exponential generating function for the $q$-analogue of alternating power sums.Comment: No comment