English
Related papers

Related papers: A spline interpretation of Eulerian numbers

200 papers

We give a new construction of q-Genocchi numbers, Euler numbers of higher order, which are different than the q-Genocchi numbers of Cangul-Ozden-Simsek. By using our q-Genoucchi, Euler nimbers of higher order, we can investigate the…

Number Theory · Mathematics 2009-01-06 Taekyun Kim

In this paper we present an efficient and robust approach to compute a normalized B-spline-like basis for spline spaces with pieces drawn from extended Tchebycheff spaces. The extended Tchebycheff spaces and their dimensions are allowed to…

Numerical Analysis · Mathematics 2020-12-08 Rene R. Hiemstra , Thomas J. R. Hughes , Carla Manni , Hendrik Speleers , Deepesh Toshniwal

We present computational methods for constructing orthogonal/orthonormal polynomials over arbitrary polygonal domains in $\mathbb{R}^2$ using bivariate spline functions. Leveraging a mature MATLAB implementation which generates spline…

Numerical Analysis · Mathematics 2026-01-08 Ming-Jun Lai

In this paper, we derive some interesting symmetric properties for the geenralized Euler numbers and polynomials.

Number Theory · Mathematics 2009-07-29 T. Kim

Univariate pseudo-splines are a generalization of uniform B-splines and interpolatory $2n$-point subdivision schemes. Each pseudo-spline is characterized as the subdivision scheme with least possible support among all schemes with specific…

Numerical Analysis · Mathematics 2017-06-12 Costanza Conti , Chongyang Deng , Kai Hormann

We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…

Combinatorics · Mathematics 2015-03-03 B. S. El-Desouky , Abdelfattah Mustafa

The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…

Number Theory · Mathematics 2021-06-29 Dae San Kim , Dmitry V. Dolgy , Hye-Kyung Kim , Hyunseok Lee , Taekyun Kim

This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and several Analysis-related applications are mentioned.

Classical Analysis and ODEs · Mathematics 2016-10-10 Khristo N. Boyadzhiev

New differential-recurrence relations for B-spline basis functions are given. Using these relations, a recursive method for finding the Bernstein-B\'{e}zier coefficients of B-spline basis functions over a single knot span is proposed. The…

Numerical Analysis · Mathematics 2024-07-22 Filip Chudy , Paweł Woźny

The aim of this paper is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential…

Number Theory · Mathematics 2022-02-11 Taekyun Kim , Dae San Kim

In this paper, we exploit the r-Stirling numbers of both kinds in order to give explicit formulae for the values of the high order Bernoulli numbers and polynomials of both kinds at integers. We give also some identities linked the…

Number Theory · Mathematics 2014-01-24 Miloud Mihoubi , Meriem Tiachachat

Article presents a short investigation into some properties of the Moser polynomials which appear in various problems from algebraic combinatorics. For instance, these polynomials can be used to solve the Generalized Moser's Problem on…

Combinatorics · Mathematics 2019-03-12 Dmitri Fomin

The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of…

Number Theory · Mathematics 2009-11-17 Boris Y. Rubinstein

In this paper we study the higher-order Euler numbers and polynomials and we introduce the mutiple zeta functions which interpolate higher-order Euler polynomials and numbers at negative integers

Number Theory · Mathematics 2010-01-12 Taekyun Kim

In this paper, we study a degenerate version of the Daehee polynomials and numbers, namely the degenerate Daehee polynomials and numbers, which were recently introduced by Jang et. al. We derive their explicit expressions and some…

Number Theory · Mathematics 2020-04-21 Taekyun Kim , Dae San Kim , Han Young Kim , Jongkyum Kwon

In this paper we present grammatical interpretations of the alternating Eulerian polynomials of types A and B. As applications, we derive several properties of the type B alternating Eulerian polynomials, including combinatorial expansions,…

Combinatorics · Mathematics 2021-06-25 Shi-Mei Ma , Qi Fang , Toufik Mansour , Yeong-Nan Yeh

In this paper we consider the approximation of a function by its interpolating multilinear spline and the approximation of its derivatives by the derivatives of the corresponding spline. We derive formulas for the uniform approximation…

Numerical Analysis · Mathematics 2013-08-27 Ryan Anderson , Yuliya Babenko , Tetiana Leskevych

Since 1950s, mathematicians have successfully interpreted the traditional Eulerian numbers and $q-$Eulerian numbers combinatorially. In this paper, the authors give a combinatorial interpretation to the general Eulerian numbers defined on…

Combinatorics · Mathematics 2014-07-01 Tingyao Xiong , Jonathan I. Hall , Hung-ping Tsao

Tangent numbers $T_{2n-1}$, which enumerate alternating permutations of odd length, play a prominent role in the Taylor series expansion of the tangent function $\tan(x)$. In this work, we adopt a combinatorial approach based on the…

Combinatorics · Mathematics 2026-03-25 Jean-Christophe Pain

In the present paper, we introduce Eulerian polynomials attached to by using p-adic q-integral on Zp . Also, we give new interesting identities via the generating functions of Dirichlet's type of Eulerian polynomials. After, by applying…

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz , Deyao Gao