Results 1 to 10 of about 682 (118)

On q-Euler Numbers Related to the Modified q-Bernstein Polynomials

Abstract and Applied Analysis, 2010
We consider q-Euler numbers, polynomials, and q-Stirling numbers of first and second kinds. Finally, we investigate some interesting properties of the modified
Min-Soo Kim, Daeyeoul Kim, Taekyun Kim
doaj   +2 more sources

Some Identities of the Twisted 𝑞-Genocchi Numbers and Polynomials with Weight 𝛼 and 𝑞-Bernstein Polynomials with Weight 𝛼

Abstract and Applied Analysis, 2011
Recently mathematicians have studied some interesting relations between 𝑞-Genocchi numbers, 𝑞-Euler numbers, polynomials, Bernstein polynomials, and 𝑞-Bernstein polynomials.
H. Y. Lee, N. S. Jung, C. S. Ryoo
doaj   +2 more sources

Generating Functions for q-Apostol Type Frobenius–Euler Numbers and Polynomials

Axioms, 2012
The aim of this paper is to construct generating functions, related to nonnegative real parameters, for q-Eulerian type polynomials and numbers (or q-Apostol type Frobenius–Euler polynomials and numbers).
Yilmaz Simsek
exaly   +3 more sources

Some identities related to degenerate Bernoulli and degenerate Euler polynomials

Mathematical and Computer Modelling of Dynamical Systems
The aim of this paper is to study degenerate Bernoulli and degenerate Euler polynomials and numbers and their higher-order analogues. We express the degenerate Euler polynomials in terms of the degenerate Bernoulli polynomials and vice versa.
Taekyun Kim, Dae San Kim
exaly   +3 more sources

A Note on Multi-Euler–Genocchi and Degenerate Multi-Euler–Genocchi Polynomials

Journal of Mathematics, 2023
Recently, the generalized Euler–Genocchi and generalized degenerate Euler–Genocchi polynomials are introduced. The aim of this note is to study the multi-Euler–Genocchi and degenerate multi-Euler–Genocchi polynomials which are defined by means of the ...
Taekyun Kim, Dae San Kim, Jin-Woo Park, Jongkyum Kwon   +3 more
doaj   +1 more source

Some Relationships between the Analogs of Euler Numbers and Polynomials

Journal of Inequalities and Applications, 2007
We construct new twisted Euler polynomials and numbers. We also study the generating functions of the twisted Euler numbers and polynomials associated with their interpolation functions.
C. S. Ryoo, Lee-Chae Jang, T. Kim
doaj   +2 more sources

Construction on the Degenerate Poly-Frobenius-Euler Polynomials of Complex Variable

Journal of Function Spaces, 2021
In this paper, we introduce degenerate poly-Frobenius-Euler polynomials and derive some identities of these polynomials. We give some relationships between degenerate poly-Frobenius-Euler polynomials and degenerate Whitney numbers and Stirling numbers of
Ghulam Muhiuddin, Waseem Ahmad Khan, Deena Al-Kadi   +2 more
doaj   +1 more source

Some identities on degenerate poly-Euler polynomials arising from degenerate polylogarithm functions

Applied Mathematics in Science and Engineering, 2023
Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This focus stems from their nascent importance for applications in combinatorics, number theory and in other aspects of applied mathematics.
Lingling Luo, Yuankui Ma, Taekyun Kim, Hongze Li   +3 more
doaj   +1 more source

Ordinary and degenerate Euler numbers and polynomials

Journal of Inequalities and Applications, 2019
In this paper, we study some identities on Euler numbers and polynomials, and those on degenerate Euler numbers and polynomials which are derived from the fermionic p-adic integrals on Zp $\mathbb{Z}_{p}$.
Taekyun Kim, Dae San Kim, Han Young Kim, Jongkyum Kwon   +3 more
doaj   +1 more source

Bernoulli F-polynomials and Fibo–Bernoulli matrices

Advances in Difference Equations, 2019
In this article, we define the Euler–Fibonacci numbers, polynomials and their exponential generating function. Several relations are established involving the Bernoulli F-polynomials, the Euler–Fibonacci numbers and the Euler–Fibonacci polynomials. A new
Semra Kuş, Naim Tuglu, Taekyun Kim
doaj   +1 more source