Carlitz's q-Bernoulli Polynomials Research Articles

Symmetry identities for generalized Carlitz's q-Bernoulli polynomials under S4

Symmetry identities for generalized Carlitz's q-Bernoulli polynomials under S4

Some new identities of symmetry for higher-order Carlitz q-Bernoulli polynomials arising from p-adic q-integral on Zp under the symmetric group of degree five

Let p be a fixed prime number. Throughout this paper Zp, Qp and Cp will denote the ring of p-adic integers, the field of p-adic rational numbers and the completion of algebraic closure of Qp. The p-adic norm is normally defined by as |p|p = 1 p . Let q be an indeterminate in Cp such that |1− q|p < p − 1 p−1 . Then the q-analogue of number x is defined as [x]q = 1−qx 1−q . Note that limq→1[x]q = x. Let UF (Zp) be the space of uniformly differentiable functions on Zp. For f ∈ UD(Zp), the p-adic q-integral is defined by Kim to be

A note on identities of symmetry for generalized Carlitz's q-Bernoulli polynomials

A note on identities of symmetry for generalized Carlitz's q-Bernoulli polynomials

A p-adic approach to identities of symmetry for Carlitz's q-Bernoulli polynomials

A p-adic approach to identities of symmetry for Carlitz's q-Bernoulli polynomials

Some symmetric identities of generalized Carlitz's q-Bernoulli polynomials of the first kind

Some symmetric identities of generalized Carlitz's q-Bernoulli polynomials of the first kind

Some identities of generalized higher-order Carlitz q-Bernoulli polynomials

In this paper, we give some interesting symmetric identities of generalized higher-order Carlitz q-Bernoulli polynomials attached to χ which are derived from symmetry properties of multivariate p-adic q-integral on X.

Identities of symmetry for Carlitz q-Bernoulli polynomials arising from q-Volkenborn integrals on Zp under symmetry group S3

Identities of symmetry for Carlitz q-Bernoulli polynomials arising from q-Volkenborn integrals on Zp under symmetry group S3

Some identities of symmetry for the higher-order Carlitz q-Bernoulli polynomials under third dihedral group D_3 arising from q-Volkenborn integral on Z_p

Some identities of symmetry for the higher-order Carlitz q-Bernoulli polynomials under third dihedral group D_3 arising from q-Volkenborn integral on Z_p

A note on Carlitz q-Bernoulli numbers and polynomials

In this article, we first aim to give simple proofs of known formulae for the generalized Carlitz q-Bernoulli polynomials βm,χ(x, q) in the p-adic case by means of a method provided by Kim and then to derive a complex, analytic, two-variable q-L-function that is a q-analog of the two-variable L-function. Using this function, we calculate the values of two-variable q-L-functions at nonpositive integers and study their properties when q tends to 1. Mathematics Subject Classification (2000): 11B68; 11S80.