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1.
广义n阶Euler-Bernoulli多项式   总被引:25,自引:2,他引:23  
本文得到了广义n阶Euler数和广义n阶Bernoulli数,广义n阶Euler多项式和广义n阶Bernoulli多项式的关系式。  相似文献   

2.
高阶Bernoulli多项式和高阶Euler多项式的关系   总被引:7,自引:0,他引:7  
雒秋明  马韵新  祁锋 《数学杂志》2005,25(6):631-636
利用发生函数的方法,讨论了高阶Bernoulli数和高阶Euler数,高阶Bernoulli多项式和高阶Euler多项式之间的关系,得到了经典Bernoulli数和Euler数,经典Bernoulli多项式和Euler多项式之间的新型关系。  相似文献   

3.
高阶Bernoulli多项式和高阶Euler多项式的新计算公式   总被引:1,自引:0,他引:1  
李志荣  李映辉 《大学数学》2008,24(3):112-116
使用发生函数方法,利用两种第一类Stirling数给出高阶Bernoulli多项式和高阶Euler多项式的简捷计算公式.  相似文献   

4.
利用广义Lucas多项式L n(x,y)的性质,通过构造组合和式T n(x,y;tx2),结合Bernoulli多项式的生成函数和Euler多项式的生成函数,采用分析学中的方法,得到两个有关L2n(x,y)的恒等式.并从这一结果出发,得到了两个推论,推广了相关文献的一些结果.  相似文献   

5.
高阶多元Euler多项式和高阶多元Bernoulli多项式   总被引:1,自引:1,他引:0  
本文给出了高阶多元Euler数和多项式与高阶多元Bernouli数和多项式的定义,讨论了它们的一些重要性质,得到了高阶多元Euler多项式(数)和高阶多元Bernouli多项式(数)的关系式·  相似文献   

6.
高阶Euler多项式的推广及其应用   总被引:1,自引:0,他引:1  
雒秋明  刘爱启 《数学杂志》2006,26(5):574-578
利用Apostol的方法,推广了高阶Euler数和多项式,得到了它们分别用第二类Stirling数和Gauss超几何函数表示的公式,最后给出了一些相应的特殊情况和应用.  相似文献   

7.
递归序列与高阶项式   总被引:7,自引:0,他引:7  
引  言关于递归序列与Euler-Bernoulli数和多项式、递归序列与高阶Euler-Bernoulli数和多项式的关系问题的研究一直是国内外许多学者感兴趣的课题,并有了许多研究成果(见[1]~[7]).本文首先对Euler-Bernoulli数和多项式、高阶Euler-Bernoulli数和多项式进行推广,提出高阶多元Euler数和多项式、高阶多元Bernoulli数和多项式的定义,然后讨论它们与递归序列的关系,文中得出的结果是P.F.Byrd[1],R.P.Kelisky[2]和Zhangzhizheng[3]的相应结果的推广和深化.2 定义和引理定义2.1 k阶s元Euler数E(k)v1…vs和k阶s元Bernoulli数B(k)v1…v…  相似文献   

8.
本文讨论了广义中心阶乘数的性质,刻画了广义中心阶乘数与高阶Euler-Bernoulli数和多项式的关系,建立了一些包含 Norlund Euler-Bernoulli多项式恒等式,推广了 Dilcher K.[1],Zhang Wenpeng[2]和 Zeitlin David[3]的结果.  相似文献   

9.
广义中心阶乘数与高阶Nrlund Euler-Bernoulli多项式   总被引:15,自引:0,他引:15  
刘国栋 《数学学报》2001,44(5):933-946
本文讨论了广义中心阶乘数的性质,刻画了广义中心阶乘数与高阶Euler-Bernoulli数和多项式的关系,建立了一些包含 Norlund Euler-Bernoulli多项式恒等式,推广了 Dilcher K.[1],Zhang Wenpeng[2]和 Zeitlin David[3]的结果.  相似文献   

10.
刘国栋 《应用数学和力学》2002,23(11):1203-1210
给出了高阶多元Noerlund Euler多项式和高阶多元Noerlund Bernoulli多项式的定义,讨论了它们的一些重要性质,建立了一些包含递归序列和上述多项式的恒等式。  相似文献   

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13.
We prove convolution identities of arbitrary orders for Bernoulli and Euler polynomials, i.e., sums of products of a fixed but arbitrary number of these polynomials. They differ from the more usual convolutions found in the literature by not having multinomial coefficients as factors. This generalizes a special type of convolution identity for Bernoulli numbers which was first discovered by Yu. Matiyasevich.  相似文献   

14.
The nth order derivatives of tan x and sec x may be represented by polynomials P n (u) and Q n (u) in u = tan x, which are known as the derivative polynomials for the tangent and secant and have occurred in diverse contexts. In this paper, explicit representations of P n (u) and Q n (u) are derived in terms of the central factorial numbers of the second kind, and the values of the Bernoulli and Euler polynomials at rationals are expressed by means of these polynomials.  相似文献   

15.
The aim of this paper is to introduce and investigate some of the primary generalizations and unifications of the Peters polynomials and numbers by means of convenient generating functions and p‐adic integrals method. Various fundamental properties of these polynomials and numbers involving some explicit series and integral representations in terms of the generalized Stirling numbers, generalized harmonic sums, and some well‐known special numbers and polynomials are presented. By using p‐adic integrals, we construct generating functions for Peters type polynomials and numbers (Apostol‐type Peters numbers and polynomials). By using these functions with their partial derivative eqautions and functional equations, we derive many properties, relations, explicit formulas, and identities including the Apostol‐Bernoulli polynomials, the Apostol‐Euler polynomials, the Boole polynomials, the Bernoulli polynomials, and numbers of the second kind, generalized harmonic sums. A brief revealing and historical information for the Peters type polynomials are given. Some of the formulas given in this article are given critiques and comments between previously well‐known formulas. Finally, two open problems for interpolation functions for Apostol‐type Peters numbers and polynomials are revealed.  相似文献   

16.
Haruki and Rassias [H. Haruki, T.M. Rassias, New integral representations for Bernoulli and Euler polynomials, J. Math. Anal. Appl. 175 (1993) 81-90] found the integral representations of the classical Bernoulli and Euler polynomials and proved them by making use of the properties of certain functional equation. In this sequel, we rederive, in a completely different way, the results of Haruki and Rassias and deduce related and new integral representations. Our proofs are quite simple and remarkably elementary.  相似文献   

17.
李桂贞 《大学数学》2006,22(4):100-103
讨论了高阶Genocchi数的性质,建立了一些包含高阶Genocchi数和高阶Euler-Bernoulli数的恒等式.  相似文献   

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