-
1
q-Genocchi Numbers and Polynomials Associated with Fermionic p-Adic Invariant Integrals on ℤp
Published 2008-01-01“…The main purpose of this paper is to present a systemic study of some families of multiple Genocchi numbers and polynomials. In particular, by using the fermionic p-adic invariant integral on ℤp, we construct p-adic Genocchi numbers and polynomials of higher order. …”
Get full text
Article -
2
Some Identities on the 𝑞-Genocchi Polynomials of Higher-Order and 𝑞-Stirling Numbers by the Fermionic 𝑝-Adic Integral on ℤ𝑝
Published 2010-01-01“…A systemic study of some families of 𝑞-Genocchi numbers and families of polynomials of Nörlund type is presented by using the multivariate fermionic 𝑝-adic integral on ℤ𝑝. …”
Get full text
Article -
3
On 𝑝-Adic Analogue of 𝑞-Bernstein Polynomials and Related Integrals
Published 2010-01-01“…The purpose of this paper is to study some properties of several type Kim's 𝑞-Bernstein polynomials to express the 𝑝-adic 𝑞-integral of these polynomials on ℤ𝑝 associated with Carlitz's 𝑞-Bernoulli numbers and polynomials. …”
Get full text
Article -
4
Symmetry Fermionic 𝑝-Adic 𝑞-Integral on ℤ𝑝 for Eulerian Polynomials
Published 2012-01-01“…Kim et al. (2012) introduced an interesting p-adic analogue of the Eulerian polynomials. They studied some identities on the Eulerian polynomials in connection with the Genocchi, Euler, and tangent numbers. …”
Get full text
Article -
5
-
6
𝑞-Bernstein Polynomials Associated with 𝑞-Stirling Numbers and Carlitz's 𝑞-Bernoulli Numbers
Published 2010-01-01“…In this paper, we give a 𝑝-adic 𝑞-integral representation for 𝑞-Bernstein type polynomials and investigate some interesting identities of 𝑞-Bernstein type polynomials associated with 𝑞-extensions of the binomial distribution, 𝑞-Stirling numbers, and Carlitz's 𝑞-Bernoulli numbers.…”
Get full text
Article -
7
Derivation of Identities Involving Bernoulli and Euler Numbers
Published 2012-01-01“…We derive some new and interesting identities involving Bernoulli and Euler numbers by using some polynomial identities and p-adic integrals on ℤ𝑝.…”
Get full text
Article -
8
Some New Identities on the Bernoulli and Euler Numbers
Published 2011-01-01“…We give some new identities on the Bernoulli and Euler numbers by using the bosonic p-adic integral on Zp and reflection symmetric properties of Bernoulli and Euler polynomials.…”
Get full text
Article -
9
Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials
Published 2009-01-01“…By the properties of p-adic invariant integral on ℤp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. …”
Get full text
Article -
10
Identities Involving q-Bernoulli and q-Euler Numbers
Published 2012-01-01“…We give some identities on the q-Bernoulli and q-Euler numbers by using p-adic integral equations on ℤp.…”
Get full text
Article -
11
On the Modified q-Bernoulli Numbers of Higher Order with Weight
Published 2012-01-01“…In particular, by using the bosonic p-adic q-integral on ℤp, we derive new identities of q-Bernoulli numbers and polynomials with weight.…”
Get full text
Article -
12
On q-Euler Numbers Related to the Modified q-Bernstein Polynomials
Published 2010-01-01“…Finally, we investigate some interesting properties of the modified q-Bernstein polynomials related to q-Euler numbers and q-Stirling numbers by using fermionic p-adic integrals on ℤp.…”
Get full text
Article -
13
Some Identities on the q-Bernoulli Numbers and Polynomials with Weight 0
Published 2011-01-01“…Recently, Kim (2011) has introduced the q-Bernoulli numbers with weight α. In this paper, we consider the q-Bernoulli numbers and polynomials with weight α=0 and give p-adic q-integral representation of Bernstein polynomials associated with q-Bernoulli numbers and polynomials with weight 0. …”
Get full text
Article -
14
A Note on q-Analogues of Degenerate Catalan-Daehee Numbers and Polynomials
Published 2022-01-01“…(Filomat J. 35 (5):17, 2022) studied q-analogues of Catalan-Daehee numbers and polynomials by making use of p-adic q-integrals on ℤp. …”
Get full text
Article -
15
A Note on the Modified q-Bernoulli Numbers and Polynomials with Weight α
Published 2011-01-01“…A systemic study of some families of the modified q-Bernoulli numbers and polynomials with weight α is presented by using the p-adic q-integration ℤp. …”
Get full text
Article -
16
Some Relations between Twisted (h,q)-Euler Numbers with Weight α and q-Bernstein Polynomials with Weight α
Published 2011-01-01“…By using fermionic p-adic q-integral on ℤp, we give some interesting relationship between the twisted (h, q)-Euler numbers with weight α and the q-Bernstein polynomials.…”
Get full text
Article -
17
Further Results on a Curious Arithmetic Function
Published 2020-01-01“…Let p be an odd prime number and n be a positive integer. Let vpn, N∗, and Q+ denote the p-adic valuation of the integer n, the set of positive integers, and the set of positive rational numbers, respectively. …”
Get full text
Article -
18
On the System of Diophantine Equations x2-6y2=-5 and x=az2-b
Published 2014-01-01“…The proof utilizes algebraic number theory and p-adic analysis which successfully avoid discussing the class number and factoring the ideals.…”
Get full text
Article -
19
A new proof of Nishioka’s theorem in Mahler’s method
Published 2023-09-01“…Working with functions of several variables and with different Mahler transformations leads to a number of complications, including the need to prove a general vanishing theorem and to use tools from ergodic Ramsey theory and Diophantine approximation (e.g., a variant of the $p$-adic Schmidt subspace theorem). …”
Get full text
Article -
20
Some Properties of Multiple Generalized q-Genocchi Polynomials with Weight and Weak Weight
Published 2012-01-01“…The present paper deals with the various q-Genocchi numbers and polynomials. We define a new type of multiple generalized q-Genocchi numbers and polynomials with weight α and weak weight β by applying the method of p-adic q-integral. …”
Get full text
Article
