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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.
D S Kim
exaly   +3 more sources

A Note on Degenerate Euler and Bernoulli Polynomials of Complex Variable [PDF]

Symmetry, 2019
D S Kim, Hyunseok Lee
exaly   +4 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).
Yılmaz Şimşek
exaly   +3 more sources

New Formulas and Connections Involving Euler Polynomials

Axioms, 2022
The major goal of the current article is to create new formulas and connections between several well-known polynomials and the Euler polynomials. These formulas are developed using some of these polynomials’ well-known fundamental characteristics as well
Waleed Mohamed Abd-Elhameed, Amr Kamel Amin   +1 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

On generalized degenerate Euler–Genocchi polynomials

Applied Mathematics in Science and Engineering, 2023
We introduce the generalized degenerate Euler–Genocchi polynomials as a degenerate version of the Euler–Genocchi polynomials. In addition, we introduce their higher-order version, namely the generalized degenerate Euler–Genocchi polynomials of order α ...
Taekyun Kim, Dae San Kim, Hye Kyung Kim
doaj   +1 more source

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

A Note on Bell-Based Apostol-Type Frobenius-Euler Polynomials of Complex Variable with Its Certain Applications

Mathematics, 2022
In this paper, we introduce new class of Bell-based Apostol-type Frobenius–Euler polynomials and investigate some properties of these polynomials. We derive some explicit and implicit summation formulas and their symmetric identities by using different ...
Noor Alam, Waseem Ahmad Khan, Cheon Seoung Ryoo   +2 more
doaj   +1 more source

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

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