Results 61 to 70 of about 442,598 (177)

Some Identities of Symmetry for the Generalized Bernoulli Numbers and Polynomials

Abstract and Applied Analysis, 2009
By the properties of p-adic invariant integral on ℤp, we establish various identities concerning the generalized Bernoulli numbers and polynomials. From the symmetric properties of p-adic invariant integral on ℤp, we give some interesting relationship ...
Taekyun Kim, Seog-Hoon Rim, Byungje Lee
doaj   +1 more source

Formulas for p-adic q-integrals including falling-rising factorials, combinatorial sums and special numbers

, 2017
The main purpose of this paper is to provide a novel approach to deriving formulas for the p-adic q-integral including the Volkenborn integral and the p-adic fermionic integral.
Simsek, Yilmaz
core  

Some Simpson- and Ostrowski-Type Integral Inequalities for Generalized Convex Functions in Multiplicative Calculus with Their Computational Analysis

Mathematics
Integral inequalities are very useful in finding the error bounds for numerical integration formulas. In this paper, we prove some multiplicative integral inequalities for first-time differentiable s-convex functions.
Xinlin Zhan, Abdul Mateen, Muhammad Toseef, Muhammad Aamir Ali   +3 more
doaj   +1 more source

Identities Involving q-Bernoulli and q-Euler Numbers

Abstract and Applied Analysis, 2012
We give some identities on the q-Bernoulli and q-Euler numbers by using p-adic integral equations on ℤp.
D. S. Kim, T. Kim, J. Choi, Y. H. Kim
doaj   +1 more source

Some Properties on the q-Euler Numbers and Polynomials

Abstract and Applied Analysis, 2012
We give some new identities on q-Euler numbers and polynomials by using the fermionic p-adic integral on ℤp.
T. Kim, S.-H. Lee
doaj   +1 more source

Some Identities on the 𝑞-Integral Representation of the Product of Several 𝑞-Bernstein-Type Polynomials

Abstract and Applied Analysis, 2011
The purpose of this paper is to give some properties of several 𝑞-Bernstein-type polynomials to express the 𝑞-integral on [0, 1] in terms of 𝑞-beta and 𝑞-gamma functions.
Taekyun Kim
doaj   +1 more source

Some Identities of the Frobenius-Euler Polynomials

Abstract and Applied Analysis, 2009
By using the ordinary fermionic p-adic invariant integral on ℤp, we derive some interesting identities related to the Frobenius-Euler polynomials.
Taekyun Kim, Byungje Lee
doaj   +1 more source

Two $$\beta $$ β -ensemble realization of $$\beta $$ β -deformed WLZZ models

European Physical Journal C: Particles and Fields
We consider a two $$\beta $$ β -ensemble realization of the series of $$\beta $$ β -deformed WLZZ matrix models. We demonstrate that such a realization involves $$\beta $$ β -deformed Harish-Chandra–Itzykson–Zuber integrals, one of them providing a ...
A. Mironov, A. Oreshina, A. Popolitov
doaj   +1 more source

Bilinear Identity for q-Hypergeometric Integrals

, 1997
18 pages, amstex.tex (ver.
openaire   +5 more sources

Identities of Symmetry for Euler Polynomials Arising from Quotients of Fermionic Integrals Invariant under

Journal of Inequalities and Applications, 2010
We derive eight basic identities of symmetry in three variables related to Euler polynomials and 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
Kim DaeSan, Park KyoungHo
doaj