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bernoulli多项式     
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  bernoulli polynomials
     The Bernoulli numbers of higher order and Bernoulli polynomials of higher order
     高阶Bernoulli数和高阶Bernoulli多项式
短句来源
     EXTENSIONS OF BERNOULLI POLYNOMIALS AND EULER-MACLAURIN FORMULAE
     Bernoulli多项式与Euler-Maclaurin公式的推广
短句来源
     The Relations of Bernoulli Polynomials and Euler Polynomials
     Bernoulli多项式和Euler多项式的关系
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     Some product identities of Bernoulli polynomials and Euler polynomials are obtained by the (elementary) method.
     利用初等方法给出了一类关于 Bernoulli数 ,Euler数 ; Bernoulli多项式 ,Euler多项式乘积和的恒等式
短句来源
     Recurrence Sequences and Higher Order Multivariable Euler Bernoulli Polynomials
     递归序列与高阶多元Euler-Bernoulli多项式
短句来源
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  bernoulli polynomial
     Some relations between Bernoulli polynomial and Eurler polynomial
     几个Bernoulli多项式和Euler多项式的关系式
短句来源
     Relationship between Bernoulli polynomial and power sum polynomial
     Bernoulli多项式与幂和多项式的关系
短句来源
     Relationship between Bernoulli polynomials and power sum polynomials was investigated. Formula of Bernoulli polynomial expressed by power sums was given,and two formally very symmetric identities were obtained in connection with the Bernoulli polynomial.
     研究了Bernoulli多项式与幂和多项式的关系,给出了用幂和表示Bernoulli多项式的一个公式,得到了关于Bernoulli多项式的形式上非常对称的两个恒等式.
短句来源
     The product of linear combination on Bernoulli polynomial and Euler polynomials is discussed first,and then some identities of the product of Bernoulli polynomial and Euler polynomials and a corollary were obtained.
     讨论了Bernou lli多项式与Eu ler多项式线性组合的乘积问题,给出了一组关于Bernou lli多项式与Eu ler多项式乘积和的恒等式及一个推论.
短句来源
     By the definitions of Bernoulli polynomial and Eurler polynomial,it was proved several relations between Bernoulli polynomial and Eurler polynomial,some identites of Bernoulli polynomial and Eurler polynomial were obtained also.
     利用Bernou lli多项式和Eurler多项式的定义,建立了Bernou lli多项式和Eu ler多项式之间的内在联系,得到了几个关于Bernou lli多项式和Eu ler多项式之间有趣的恒等式.
短句来源
  bernoulli multinomial
     Identical Equation of Bernoulli Multinomial and Eurler Multinomial
     有关Bernoulli多项式和Eurler多项式的恒等式
短句来源
     This article is a study of Bernoulli multinomial and Eurler multinomial, and by making use of functional relationship, reveals the inherent relation between the two types of multinomial, and wherefrom obtains a set of interesting identical equations.
     本文研究了Bernoulli多项式和Eurler多项式 ,利用函数关系式 ,揭示了两类多项式之间的内在联系 ,由此得到了一组有趣的恒等式
短句来源
  bernoulli ' s polynomial
     Higher-Order Multivariable Euler's Polynomial and Higher-Order Multivariable Bernoulli's Polynomial
     高阶多元Euler多项式和高阶多元Bernoulli多项式
短句来源
     In this paper, we gave the recursion relations on the coefficients of the Bernoulli's polynomial, reduced the calculation of the Bernoulli's polynomial and Bernoulli's numbers, at the same time, gave some fine properties of the Bernoulli's polynomial.
     给出了 Bernoulli多项式系数的递推关系式 ,简化了 Bernoulli多项式和 Bernoulli数的计算 ,同时给出了 Bernoulli多项式的一些很好的性质
短句来源

 

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      bernoulli polynomials
    Instead of Bernoulli numbers and Bernoulli polynomials, special numbers Pn and special polynomials Pn(x) introduced by Korobov in 1996 appear in the formula.
          
    Based on asymptotic analysis of the coefficients fk, an expansion of pFp-1 is constructed as a combination of the functions ζ(α, s) with explicit coefficients expressed in terms of the generalized Bernoulli polynomials.
          
    Kupershmidt constructed reflection symmetries of q-Bernoulli polynomials (see [12]).
          
    In this paper, we construct a twisted q-partial zeta function and some twisted two-variable q-L-functions that interpolate q-Bernoulli numbers, βn,ξ(h)(q), and Bernoulli polynomials, βn,x,ξ(h)(x, q), respectively, at negative integers.
          
    In the present paper, we obtain two new formulas of the Apostol-Bernoulli polynomials (see On the Lerch Zeta function.
          
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      bernoulli polynomial
    Furthermore, letψk denote the lperiodic Bernoulli polynomial of orderk∈?(k?2).
          
    Using q-Bernoulli number of higher order, we give the formula for sums of products of Carlitz's q-Bernoulli numbers of the form where is the Carlitz's q-Bernoulli polynomial.
          
      bernoulli ' s polynomial
    Higher-order multivariable euler's polynomial and higher-order multivariable bernoulli's polynomial
          
    As a result, the mathematical relationship between higher-order multivariable Euler's polynomial (numbers) and higher-order multivariable Bernoulli's polynomial (numbers) are thus obtained.
          


    In this paper, the local asymtotic behavior of (0. 3) quilltic lacunary inte- rpolation splines and their derivatives are discussed. It is shown bere that the asymptotic behayior is independent of the boundary conditions

    本文讨论[1]中所定义的五次(0,3)类缺插值样条Sn(x),当f∈cθ[0,1]时,的局部渐近性质。得到: 定理 设f(x)∈Cθ[0,1],Sn(x)是f(x)的五次(0,3)类(i)型缺插值样条,=Ⅰ,Ⅱ,Ⅲ,Ⅳ,那么对于任意固定的x∈(0,1),当 n→时有 Sn(x)=f(x)-[Bθ(u)-1/42]·f(6)(x)·h6/6!+o(h6)和 Sn(r)(x)==f(r)(x)-B6-r(u)f(6)(x)·h6-r/(6-r)!+o(h6-r),r=1,2,3,4,5。其中B1(u)是首项系数为1的j次Bernoulli多项式;u=(x-γh)i γ=[nx]。

    Let △n={i/n=X_1 be a uniform partition of [0, 1] and f be a function satisfying f∈C~(2m+1)[0, 1]. The even spline associated with f and △n is. defined by the conditions:ⅰ) S(x_i+1/2)=f(x_i+1/2) i=0, 1, …, n-1;ⅱ) S~(α)(0)=f(α)(0), S~(α)(1)=f~(α)(1), α=0, 2, …, 2m-2, where x_1+1/2=x_i+h/2, h=1/n. We denote E=f-S and proved following Theorem A. Let f∈C~(2m+1), m=1, 2, x∈(x_i, x_i+1) then: E~(r)(x)=f~(r)(x)-S~(r)(x) (?) where |Q_r(x)|≤C_rh~(2m+1-r). ω(f~(2m+1), h), B_n(t) denote Bernoulli polynomials.

    本文证明偶次(二、四次L型)样条插值,于一类Bernoulli多项式的零点上具有高一阶的精度,并附有一个数值结果。

    Wegener's kernel theorem and trigonometric series of Bernoulli polynomialsare used to obtain the

    利用Wegener核定理、Bernoulli多项式的三角级数展开,得到权函数为1的任意区间上的复化Gauss型求积公式的渐近展开式,它只含h的偶次幂项。

     
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