Results 11 to 20 of about 799 (105)

Explicit Formulas involving q-Euler Numbers and Polynomials [PDF]

Abstract and Applied Analysis, Volume 2012, Issue 1, 2012., 2012
In this paper, we deal with q-Euler numbers and q-Bernoulli numbers. We derive some interesting relations for q-Euler numbers and polynomials by using their generating function and derivative operator.
Acikgoz, Mehmet, Araci, Serkan, Seo, Jong Jin   +2 more
core   +5 more sources

Some Identities on Bernoulli and Euler Numbers

Discrete Dynamics in Nature and Society, 2012
Recently, Kim introduced the fermionic p-adic integral on Zp. By using the equations of the fermionic and bosonic p-adic integral on Zp, we give some interesting identities on Bernoulli and Euler numbers.
D. S. Kim, T. Kim, J. Choi, Y. H. Kim
doaj   +2 more sources

Several Symmetric Identities of the Generalized Degenerate Fubini Polynomials by the Fermionic p-Adic Integral on Zp

Symmetry
After constructions of p-adic q-integrals, in recent years, these integrals with some of their special cases have not only been utilized as integral representations of many special numbers, polynomials, and functions but have also given the chance for deep analysis of many families of special polynomials and numbers, such as Bernoulli, Fubini, Bell ...
Maryam Salem Alatawi, Waseem Ahmad Khan, Uğur Duran   +2 more
exaly   +3 more sources

Symmetric Identities Involving the Extended Degenerate Central Fubini Polynomials Arising from the Fermionic p-Adic Integral on ℤ_p

Axioms
Since the constructions of p-adic q-integrals, these integrals as well as particular cases have been used not only as integral representations of many special functions, polynomials, and numbers, but they also allow for deep examinations of many families
Maryam Salem Alatawi, Waseem Ahmad Khan, Ugur Duran   +2 more
doaj   +4 more sources

Asymptotic Expansions for Large Degree Tangent and Apostol‐Tangent Polynomials of Complex Order

Journal of Applied Mathematics, Volume 2023, Issue 1, 2023., 2023
This paper provides asymptotic expansions for large values of n of tangent Tnμz and Apostol‐tangent Tnμz;λ polynomials of complex order. The derivation is done using contour integration with the contour avoiding branch cuts.
Cristina B. Corcino, Roberto B. Corcino, Jeremar Casquejo, Tudor Barbu   +3 more
wiley   +1 more source

Identities of Degenerate Poly‐Changhee Polynomials Arising from λ‐Sheffer Sequences

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
In the 1970s, Gian‐Carlo Rota constructed the umbral calculus for investigating the properties of special functions, and by Kim‐Kim, umbral calculus is generalized called λ‐umbral calculus. In this paper, we find some important relationships between degenerate Changhee polynomials and some important special polynomials by expressing the Changhee ...
Sang Jo Yun, Jin-Woo Park, Barbara Martinucci   +2 more
wiley   +1 more source

A Computational Model for q‐Bernstein Quasi‐Minimal Bézier Surface

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
A computational model is presented to find the q‐Bernstein quasi‐minimal Bézier surfaces as the extremal of Dirichlet functional, and the Bézier surfaces are used quite frequently in the literature of computer science for computer graphics and the related disciplines.
Daud Ahmad, M. Khalid Mahmood, Qin Xin, Ferdous M. O. Tawfiq, Sadia Bashir, Arsha Khalid, Muhammad Kamran Jamil   +6 more
wiley   +1 more source

On Carlitz's Type q-Euler Numbers Associated with the Fermionic P-Adic Integral on ℤp

Journal of Inequalities and Applications, 2010
Min-Soo Kim, Taekyun Kim, Cheon-Seoung Ryoo   +2 more
doaj   +2 more sources

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

Symmetry, 2018
We study a q-analogue of Euler numbers and polynomials naturally arising from the p-adic fermionic integrals on Zp and investigate some properties for these numbers and polynomials. Then we will consider p-adic fermionic integrals on Zp of the two variable q-Bernstein polynomials, recently introduced by Kim, and demonstrate that they can be written in ...
Lee-Chae Jang, Taekyun Kim 0001, Dae San Kim, Dmitry V. Dolgy   +3 more
openaire   +1 more source

A Note on q‐Analogues of Degenerate Catalan‐Daehee Numbers and Polynomials

Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022
Recently, Yuankui et al. (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. Motivated by this study, we consider q‐analogues of degenerate Catalan‐Daehee numbers and polynomials with the help of p‐adic q‐integrals on ℤp. By using their generating function, we derive some
Waseem A. Khan, Barbara Martinucci
wiley   +1 more source