共查询到20条相似文献,搜索用时 22 毫秒
1.
《Indagationes Mathematicae (Proceedings)》1982,85(4):415-422
Among polynomials in several variables of given form, the Laguerre and Hermite polynomials are recovered. This is obtained by requiring that the polynomials in several variables satisfy known properties characterizing the classical polynomials.Analogous characterizations of the Meixner polynomials are likewise determined. These are based on the characteristic properties of the Meixner polynomials recently established.All new properties generalize the previous ones. 相似文献
2.
David W Boyd 《Journal of Number Theory》1981,13(1):116-121
Mahler defined the measure of a polynomial in several variables to be the geometric mean of the modulus of the polynomial averaged over the torus. The classical theorem of Kronecker which characterizes monic polynomials with integer coefficients all of whose roots are inside the unit disk can be regarded as characterizing those polynomials of one variable whose measure is exactly 1. Here this result is generalized to polynomials in several variables. The method employed also gives easy generalizations of recent results of Schinzel and Dobrowolski on Lehmer's problem. 相似文献
3.
In this paper we first solve a convolution integral equation involving product of the general class of polynomials and theH-function of several variables. Due to general nature of the general class of polynomials and theH-function of several variables which occur as kernels in our main convolution integral equation, we can obtain from it solutions of a large number of convolution integral equations involving products of several useful polynomials and special functions as its special cases. We record here only one such special case which involves the product of general class of polynomials and Appell's functionF 3. We also give exact references of two results recently obtained by Srivastavaet al [10] and Rashmi Jain [3] which follow as special cases of our main result. 相似文献
4.
Mathematical Notes - We obtain a generalization of the Aron-Hájek theorem about the null subspaces of homogeneous odd polynomials (in several variables) to the case of arbitrary odd polynomials. 相似文献
5.
This paper deals with some qualitative properties of orthogonal polynomials in several variables. The boundedness and relations between two sets of orthonormal polynomials associated with an arbitrary weight function and its extension are investigated. It presents an analogy to Korous' result for general orthogonal polynomials in one variable. 相似文献
6.
J. F. van Diejen 《Transactions of the American Mathematical Society》1999,351(1):233-270
Limiting cases are studied of the Koornwinder-Macdonald multivariable generalization of the Askey-Wilson polynomials. We recover recently and not so recently introduced families of hypergeometric orthogonal polynomials in several variables consisting of multivariable Wilson, continuous Hahn and Jacobi type polynomials, respectively. For each class of polynomials we provide systems of difference (or differential) equations, recurrence relations, and expressions for the (squared) norms of the polynomials in question.
7.
H. B. Coonce 《Aequationes Mathematicae》1996,52(1):201-214
Summary The power functions and the Chebyshev polynomials are examples of families of permutable functions. Recently it was shown how to generalize this idea to polynomials of several variables. In this article the restriction of being polynomials is removed. It is shown how to make a ring and then a field of permutable functions of several variables. The uniqueness problem is discussed. 相似文献
8.
In this paper we will define the order and type of basic and composite sets of polynomials of several complex variables in complete Reinhardt domains. Also, the property
of basic and composite sets of polynomials of several complex variables in complete Reinhardt domains is discussed. 相似文献
9.
T. Yu. Kulikova 《Mathematical Notes》2010,88(5-6):855-859
The author’s results concerning the null subspaces of arbitrary odd polynomials in several variables are generalized to the case of common null subspaces for several odd polynomials as well as to the complex case. 相似文献
10.
NICOLAE CIPRIAN BONCIOCAT ALEXANDRU ZAHARESCU 《Proceedings Mathematical Sciences》2011,121(2):133-141
We provide several irreducibility criteria for multivariate polynomials and methods to construct irreducible polynomials starting
from irreducible polynomials in fewer variables. 相似文献
11.
Invariant factors of bivariate orthogonal polynomials inherit most of the properties of univariate orthogonal polynomials and play an important role in the research of Stieltjes type theorems and location of common zeros of bivariate orthogonal polynomials. The aim of this paper is to extend our study of invariant factors from two variables to several variables. We obtain a multivariate Stieltjes type theorem, and the relationships among invariant factors, multivariate orthogonal polynomials and the corresponding Jacobi matrix. We also study the location of common zeros of multivariate orthogonal polynomials and provide some examples of tri-variate. 相似文献
12.
Mehmet Aç?kgöz 《Applied mathematics and computation》2011,218(3):707-712
In this paper, we consider the modified q-Bernstein polynomials for functions of several variables on q-Volkenborn integral and investigate some new interesting properties of these polynomials related to q-Stirling numbers, Hermite polynomials and Carlitz’s type q-Bernoulli numbers. 相似文献
13.
The evaluation of a polynomial at several points is called the problem of multi-point evaluation. Sometimes, the set of evaluation points is fixed and several polynomials need to be evaluated at this set of points. Several efficient algorithms for this kind of “amortized” multi-point evaluation have been developed recently for the special cases of bivariate polynomials or when the set of evaluation points is generic. In this paper, we extend these results to the evaluation of polynomials in an arbitrary number of variables at an arbitrary set of points. We prove a softly linear complexity bound when the number of variables is fixed. Our method relies on a novel quasi-reduction algorithm for multivariate polynomials, that operates simultaneously with respect to several orderings on the monomials. 相似文献
14.
Mumtaz Ahmad Khan Abdul Hakim KhanNaeem Ahmad 《Applied mathematics and computation》2012,218(11):6385-6390
The present paper deals with an extension of certain results obtained by Burchnall for Hermite polynomials to similar results for Hermite polynomials of several variables. 相似文献
15.
Recently, Chan, Chyan and Srivastava [W.-C.C. Chan, C.-J. Chyan, H.M. Srivastava, The Lagrange polynomials in several variables, Integral Transform. Spec. Funct. 12 (2001) 139-148] introduced and systematically investigated the Lagrange polynomials in several variables. In the present paper, we derive various families of multilinear and multilateral generating functions for the Chan-Chyan-Srivastava multivariable polynomials. 相似文献
16.
Nicolae Ciprian Bonciocat 《Journal of Pure and Applied Algebra》2008,212(10):2338-2343
We provide several methods to construct irreducible multivariate polynomials from irreducible polynomials in a smaller number of variables. 相似文献
17.
María Álvarez de Morales Lidia Fernández Teresa E. Pérez Miguel A. Piñar 《Journal of Computational and Applied Mathematics》2008
Differential properties for orthogonal polynomials in several variables are studied. We consider multivariate orthogonal polynomials whose gradients satisfy some quasi-orthogonality conditions. We obtain several characterizations for these polynomials including the analogues of the semiclassical Pearson differential equation, the structure relation and a differential-difference equation. 相似文献
18.
Gabriel Bengochea 《代数通讯》2013,41(7):3086-3095
We prove that the cofinite dual of the Hopf algebra of polynomials in several variables can be represented as a Hopf algebra ? of exponential polynomials that contains the polynomials as a Hopf subalgebra. We also present some algebras isomorphic to ? whose elements are rational functions or multi-sequences. 相似文献
19.
G. I. Prizva 《Journal of Mathematical Sciences》1993,66(5):2484-2487
A system of orthogonal polynomials of several discrete variables associated with the negative polynomial distribution is constructed and analyzed. The explicit form of the polynomials and the generating function are obtained.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 65, pp. 46–51, 1988. 相似文献
20.
A. B. Shidlovskii 《Mathematical Notes》2000,68(5-6):644-651
The paper presents several theorems on the linear and algebraic independence of the values at algebraic points of the set of E-functions related by algebraic equations over the field of rational functions, as well as some estimates of the absolute values of polynomials with integer coefficients in the values of such functions. The results are obtained by using the properties of ideals in the ring of polynomials of several variables formed by equations relating the above functions over the field of rational functions. 相似文献