q-Bernoulli numbers and q-Bernoulli polynomials revisited

Ryoo, C. S.; Kim, Taekyun; Lee, Byungje

doi:10.1186/1687-1847-2011-33

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Q-analog Of the Two-variable L-function (In ℂ)2

Introduction2

Introduction Definitions and Notations1

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Cited by 4 publications

(5 citation statements)

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“…The formula of Proposition 3.2 is slight extension of the result in [19] and [11,Theorem 2]. Theorem 3.3.…”

Section: Q-analog Of the Two-variable L-function (In ℂ)mentioning

confidence: 71%

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A note on Carlitz q-Bernoulli numbers and polynomials

Kim

2012

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In this article, we first aim to give simple proofs of known formulae for the generalized Carlitz q-Bernoulli polynomials b m,c (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-Lfunction 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.

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“…The formula of Proposition 3.2 is slight extension of the result in [19] and [11,Theorem 2]. Theorem 3.3.…”

Section: Q-analog Of the Two-variable L-function (In ℂ)mentioning

confidence: 71%

“…where the B m,c (x) are the mth generalized Bernoulli polynomials (e.g., [14,19]). This completes the proof.…”

Section: Q-analog Of the Two-variable L-function (In ℂ)mentioning

confidence: 99%

A note on Carlitz q-Bernoulli numbers and polynomials

Kim

2012

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“…As is well known, the classical Bernstein polynomial of order n for f ∈ C[0, 1] is defined by (see [1][2][3]),…”

Section: Introductionmentioning

confidence: 99%

On p-Adic Fermionic Integrals of q-Bernstein Polynomials Associated with q-Euler Numbers and Polynomials †

et al. 2018

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We study a q-analogue of Euler numbers and polynomials naturally arising from the p-adic fermionic integrals on Z p and investigate some properties for these numbers and polynomials. Then we will consider p-adic fermionic integrals on Z p of the two variable q-Bernstein polynomials, recently introduced by Kim, and demonstrate that they can be written in terms of the q-analogues of Euler numbers. Further, from such p-adic integrals we will derive some identities for the q-analogues of Euler numbers.

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“…Based on the observation on (1.8), the q-Hurwitz zeta function can be defined by (see, e.g., [24]) .…”

Section: Introductionmentioning

confidence: 99%