Results 21 to 30 of about 1,211 (149)
Combinatorial proofs of some properties of tangent and Genocchi numbers [PDF]
European Journal of Combinatorics, 2018 The tangent number $T_{2n+1}$ is equal to the number of increasing labelled complete binary trees with $2n+1$ vertices. This combinatorial interpretation immediately proves that $T_{2n+1}$ is divisible by $2^n$.
Han, Guo-Niu, Liu, Jing-Yi
core +5 more sources
The homogenized Linial arrangement and Genocchi numbers
Combinatorial Theory, 2022 33 pages, 10 figures.
Lazar, Alexander, Wachs, Michelle L.
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Representation by Degenerate Genocchi Polynomials
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 The aim of this study is to represent any polynomial in terms of the degenerate Genocchi polynomials and more generally of the higher‐order degenerate Genocchi polynomials. We derive explicit formulas with the help of umbral calculus and illustrate our results with some examples.
Taekyun Kim +4 more
wiley +1 more source
Generalized Fubini Apostol‐Type Polynomials and Probabilistic Applications
International Journal of Mathematics and Mathematical Sciences, Volume 2022, Issue 1, 2022., 2022 The paper aims to introduce and investigate a new class of generalized Fubini‐type polynomials. The generating functions, special cases, and properties are introduced. Using the generating functions, various interesting identities, and relations are derived. Also, special polynomials are obtained from the general class of polynomials.
Rabab S. Gomaa +2 more
wiley +1 more source
A Specific Method for Solving Fractional Delay Differential Equation via Fraction Taylor’s Series
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 It is well known that the appearance of the delay in the fractional delay differential equation (FDDE) makes the convergence analysis very difficult. Dealing with the problem with the traditional reproducing kernel method (RKM) is very tricky. The feature of this paper is to gain a more credible approximate solution via fractional Taylor’s series (FTS).
Ming-Jing Du, Ahmed Salem
wiley +1 more source
Gamma-Positivity for a Refinement of Median Genocchi Numbers
The Electronic Journal of Combinatorics, 2022 We study the generating function of descent numbers for the permutations with descent pairs of prescribed parities, the distribution of which turns out to be a refinement of median Genocchi numbers. We prove the $\gamma$-positivity for the polynomial and derive the generating function for the $\gamma$-vectors, expressed in the form of continued ...
Eu, Sen-Peng +3 more
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Numerical Approach for Solving the Fractional Pantograph Delay Differential Equations
Complexity, Volume 2022, Issue 1, 2022., 2022 A new class of polynomials investigates the numerical solution of the fractional pantograph delay ordinary differential equations. These polynomials are equipped with an auxiliary unknown parameter a, which is obtained using the collocation and least‐squares methods.
Jalal Hajishafieiha +2 more
wiley +1 more source
Unification of Two‐Variable Family of Apostol‐Type Polynomials with Applications
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 In this paper, the two‐variable unified family of generalized Apostol‐type polynomials is introduced, and some implicit forms and general symmetry identities are derived. Also, we obtain new degenerate Apostol‐type numbers and polynomials constructed from the new 2‐variable unified family.
Beih S. El-Desouky +3 more
wiley +1 more source
q-EXTENSIONS OF GENOCCHI NUMBERS
Journal of the Korean Mathematical Society, 2006 The classical Genocchi numbers, \(G_{n}\) are defined by means of the following generating function: \(((2t)/(e^{t}+1))=\sigma_{n=0}^{\infty}G_{n}((t^{n})/(n!))\), where \(G_{1}=1, G_{3}=G_{5} =G_{7}= \dots =0\). Relations between Genocchi numbers, Bernoulli numbers and Euler polynomials are given by \(G_{n} = (2-2^{n + 1})B_{n} = 2nE_{2n-1}(0 ...
Cenkci, Mehmet, Can, Mümün, Kurt, Veli
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A note on degenerate poly-Genocchi numbers and polynomials
Advances in Difference Equations, 2020 Recently, some mathematicians have been studying a lot of degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our research is also interested in this field.
Hye Kyung Kim, Lee-Chae Jang
doaj +1 more source