关于包含Hermite—Laguerre多项式的恒等式

通过讨论一类函数的高阶导数,建立了一些包含Hermite-Laguerre多项式的恒等式,推广了名的Cauchy-Sheehan组合恒等式。     

关于微分算子的若干恒等式与Hermite多项式

通过求解一个偏微分方程，得到了若干微分算子恒等式．利用这些恒等式，很自然地推出了关于Ｈｅｒｍｉｔｅ多项式的一些著名结果．     

一类包含Bernoulli多项式的恒等式的计算公式

本文给出了sum from (a_1+a_2+…a_k)=n to ((B_(a_1)(x)B_(a_2)(x)…B_(a_k)(x))/(a_1!a_2!…a_k!))的求和计算公式,其中B_i(x)为i次Bernoulli多项式,nZ≥k为正整数,。l+a2+…+ak‘n表示对所有满足该式的^维正整数组(a_1+a_2+…a_k)求和。     

一些包含契贝谢夫多项式的恒等式

讨论了著名的契贝射夫多项式的一些性质,并给出了一些有趣的恒等式。     

关于包含奇-偶下标第二类契贝谢夫多项式的恒等式

给出了一类包含偶下标第二类契贝谢夫多项式和一类包含奇下标第二类契贝谢夫多项式求和的递推公式，得到了一些包含偶下标第二类契贝谢夫多项式和奇下标第二类契贝谢夫多项式的恒等式．     

一类与多项式相关的组合恒等式

一类与多项式相关的组合恒等式王良成（四川省达县师专６３５０００）本文给出一类与多项式相关的组合恒等式，由此可以产生许多有用的组合恒等式．定理设是１＋１次多项式，则证明１°当ｎ－１，即ｆ（ｘ）＝ａｘ２＋ｂｘ＋ｃ０时，则即（１）式成立．２°假设ｎ＝ｋ，即...     

一些包含Lucas数的恒等式

利用第一类Chebyshev多项式的性质以及其与Lucas数的关系得到了关于Lucas数立方的一些恒等式.     

一类多项式恒等式及其推广

首先利用母函数法和多项式理论证明了一类多项式恒等式,接着通过求导和积分的方式得到一些新的多项式恒等式,最后给出这些恒等式的特殊形式及其应用.     

关于Bell多项式及其它的一些恒等式

本文引入了一个新的多项式,即Bell多项式.利用初等数论及组合方法,证明了包含该多项式的一些恒等式.作为这些恒等式的应用,给出了关于Bell数的同余式.     

关于两类广义多项式的一些恒等式(英文)

By means of generating function and partial derivative methods, we investigate and establish several general summation formulas involving two classes of polynomials. The general results would apply to yield some identities for the Pell polynomials and Pell-Lucas polynomials, and other general polynomials can also be recovered in this paper.     

若干包含Laguerre多项式的等式和同余式

令L_n(x)为Laguerre多项式,即L_0(x)=1,L_1(x)=-x+1,且对所有整数n≥1,有递推公式L_(n+1)(x)=(2n+1-x)L_n(x)-n~2L_(n-1)(x).主要使用组合及初等方法研究一类包含L_n(x)的卷积和式,给出其有趣的计算公式,并得到一些包含Laguerre多项式的等式和同余式,这些结果均有着重要的应用.     

A New Integral Involving the Product of Bessel Functions and Associated Laguerre Polynomials

A new result for integrals involving the product of Bessel functions and Associated Laguerre polynomials is obtained in terms of the hypergeometric function. Some special cases of the general integral lead to interesting finite and infinite series representations of hypergeometric functions.     

Zero Distribution of Composite Polynomials and Polynomials Biorthogonal to Exponentials

We analyze polynomials P _n that are biorthogonal to exponentials , in the sense that

Some Identities Involving Square of Fibonacci Numbers and Lucas Numbers

By studying the properties of Chebyshev polynomials, some specific and meaningful identities for the calculation of square of Chebyshev polynomials, Fibonacci numbers and Lucas numbers are obtained.     

关于高阶Genocchi数和广义Lucas多项式的恒等式

利用组合数学的方法,得到了一些包含高阶Genocchi数和广义Lucas多项式的恒等式,并且由此建立了Fibonacci数与Riemann Zeta函数的关系式.     

Asymptotic Approximations between the Hahn-Type Polynomials and Hermite, Laguerre and Charlier Polynomials

It has been shown in Ferreira et al. (Adv. Appl. Math 31:61–85, [2003]), López and Temme (Methods Appl. Anal. 6:131–196, [1999]; J. Cpmput. Appl. Math. 133:623–633, [2001]) that the three lower levels of the Askey table of hypergeometric orthogonal polynomials are connected by means of asymptotic expansions. In this paper we continue with that investigation and establish asymptotic connections between the fourth level and the two lower levels: we derive twelve asymptotic expansions of the Hahn, dual Hahn, continuous Hahn and continuous dual Hahn polynomials in terms of Hermite, Charlier and Laguerre polynomials. From these expansions, several limits between polynomials are derived. Some numerical experiments give an idea about the accuracy of the approximations and, in particular, about the accuracy in the approximation of the zeros of the Hahn, dual Hahn, continuous Hahn and continuous dual Hahn polynomials in terms of the zeros of the Hermite, Charlier and Laguerre polynomials.      

一些包含勒让德多项式的积分恒等式

设P_n(x)表示勒让德多项式.即就是P_0(x)=1,P_1(x)=x,当n≥2时有递推关系,P_(n+1)(x)=(2n+1)/(n+1)·xP_n(x)-n/(n+1)·P_(n-1)(x).主要目的是运用初等方法以及幂级数的性质讨论一类包含P_(n)(x)的卷积的定积分计算问题,并给出一些确切的计算公式.     

New Identities for Hall-Littlewood Polynomials and Applications

Starting from Macdonald's summation formula of Hall-Littlewood polynomials over bounded partitions and its even partition analogue, Stembridge (Trans. Amer. Math. Soc., 319(2), (1990) 469–498) derived sixteen multiple q-identities of Rogers–Ramanujan type. Inspired by our recent results on Schur functions (Adv. Appl. Math., 27, (2001) 493–509) and based on computer experiments we obtain two further such summation formulae of Hall-Littlewood polynomials over bounded partitions and derive six new multiple q-identities of Rogers–Ramanujan type. 2000 Mathematics Subject Classification: Primary–05A19; Secondary–05A17, 05A30     

q-差分内积中的小q-Jacobi-Sobolev多项式

本文讨论了关于以下内积的正交多项式 :〈p(x) ,r(x)〉( u0 ,u(α,β) ) =∑∞k=0p(qk) r(qk) (qk-c) ak(b) k(q) k +λ∑∞k=0(Dqp) (qk) (Dqr) (qk) (aq) k(bq) k(q) k给出了它的一些代数性质以及和小 q-Jacobi多项式的关系 ,得到了在 C\([0 ,1 ]∪ H )的紧子集上Qn(x)P(α- 1,β- 1)n (x) n和 Pn(x)P(α- 1,β- 1)n (x) n的相对渐近性质 .其中 Qn(x)是 n次的小 q -Jacobi-Sobolev正交多项式 ,P(α- 1,β- 1)n (x)和 Pn(x)分别是关于线性泛函 u(α- 1,β- 1)和 u0 的首一的 n次正交多项式 .