共查询到20条相似文献,搜索用时 46 毫秒
1.
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
2.
Maurice M. Mizrahi 《Journal of Computational and Applied Mathematics》1975,1(3):137-140
Hermite polynomials of several variables are defined by a generalization of the Rodrigues formula for ordinary Hermite polynomials. Several properties are derived, including the differential equation satisfied by the polynomials and their explicit expression. An application is given. 相似文献
3.
Hermite polynomials of several variables are defined by a generalization of the Rodrigues formula for ordinary Hermite polynomials. Several properties are derived, including the differential equation satisfied by the polynomials and their explicit expression. An application is given. 相似文献
4.
Subuhi Khan Ahmed Ali Al-Gonah Ghazala Yasmin 《Journal of Mathematical Analysis and Applications》2012,390(1):197-207
In this paper, a new generalized form of the Gegenbauer polynomials is introduced by using the integral representation method. Further, the Hermite–Gegenbauer and the Laguerre–Gegenbauer polynomials are introduced by using the operational identities associated with the generalized Hermite and Laguerre polynomials of two variables. 相似文献
5.
Yuan Xu 《Integral Transforms and Special Functions》2015,26(2):134-151
Orthogonal polynomials of two real variables can often be represented in complex variables. We explore the connection between the two types of representations and study the structural relations of complex orthogonal polynomials. The complex Hermite orthogonal polynomials and the disk polynomials are used as illustrating examples. 相似文献
6.
In 1952 Lee and Yang proposed the program of analyzing phase transitions in terms of zeros of partition functions. Linear operators preserving non-vanishing properties are essential in this program and various contexts in complex analysis, probability theory, combinatorics, and matrix theory. We characterize all linear operators on finite or infinite-dimensional spaces of multivariate polynomials preserving the property of being non-vanishing whenever the variables are in prescribed open circular domains. In particular, this solves the higher dimensional counterpart of a long-standing classification problem originating from classical works of Hermite, Laguerre, Hurwitz and Pólya-Schur on univariate polynomials with such properties. 相似文献
7.
V. Ya. Galkin 《Computational Mathematics and Modeling》1997,8(2):194-204
The probability function of a generalized Poisson distribution is written in terms of modified Hermite polynomials of 2nd
kind in many variables. Their relationship is established with special polynomials previously derived for this purpose. The
properties of the polynomials and the probability function are studied.
Translated from Chislennye Metody v Matematicheskoi Fizike, Published by Moscow University, Moscow, 1996. pp. 160–169. 相似文献
8.
本文利用渐近于Gauss函数的函数类?,给出渐近于Hermite正交多项式的一类Appell多项式的构造方法,使得该序列与?的n阶导数之间构成了一组双正交系统.利用此结果,本文得到多种正交多项式和组合多项式的渐近性质.特别地,由N阶B样条所生成的Appell多项式序列恰为N阶Bernoulli多项式.从而,Bernoulli多项式与B样条的导函数之间构成了一组双正交系统,且标准化之后的Bernoulli多项式的渐近形式为Hermite多项式.由二项分布所生成的Appell序列为Euler多项式,从而,Euler多项式与二项分布的导函数之间构成一组双正交系统,且标准化之后的Euler多项式渐近于Hermite多项式.本文给出Appell序列的生成函数满足的尺度方程的充要条件,给出渐近于Hermite多项式的函数列的判定定理.应用该定理,验证广义Buchholz多项式、广义Laguerre多项式和广义Ultraspherical(Gegenbauer)多项式渐近于Hermite多项式的性质,从而验证超几何多项式的Askey格式的成立. 相似文献
9.
ON HERMITE MATRIX POLYNOMIALS AND HERMITE MATRIX FUNCTIONS 总被引:1,自引:0,他引:1
In this paper properties of Hermite matrix polynomials and Hermite matrix functions are studied. The concept ot total set with respect to a matrix functional is introduced and the total property of the Hermite matrix polynomials is proved. Asymptotic behaviour of Hermite matrix polynomials is studied and the relationship of Hermite matrix functions with certain matrix differential equations is developed. A new expression of the matrix exponential for a wide class of matrices in terms of Hermite matrix polynomials is proposed. 相似文献
10.
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
11.
We prove a generalization of the Kibble–Slepian formula (for Hermite polynomials) and its unitary analogue involving the 2D Hermite polynomials recently proved in [16]. We derive integral representations for the 2D Hermite polynomials which are of independent interest. Several new generating functions for 2D q-Hermite polynomials will also be given. 相似文献
12.
A global asymptotic analysis of orthogonal polynomials via the Riemann-Hilbert approach is presented,with respect to the polynomial degree.The domains of uniformity are described in certain phase variables.A resurgence relation within the sequence of Riemann-Hilbert problems is observed in the procedure of derivation.Global asymptotic approximations are obtained in terms of the Airy function.The system of Hermite polynomials is used as an illustration. 相似文献
13.
We study Wronskians of Hermite polynomials labeled by partitions and use the combinatorial concepts of cores and quotients to derive explicit expressions for their coefficients. These coefficients can be expressed in terms of the characters of irreducible representations of the symmetric group, and also in terms of hook lengths. Further, we derive the asymptotic behavior of the Wronskian Hermite polynomials when the length of the core tends to infinity, while fixing the quotient. Via this combinatorial setting, we obtain in a natural way the generalization of the correspondence between Hermite and Laguerre polynomials to Wronskian Hermite polynomials and Wronskians involving Laguerre polynomials. Lastly, we generalize most of our results to polynomials that have zeros on the p-star. 相似文献
14.
Ridha Sfaxi 《Acta Appl Math》2011,113(3):305-321
In this paper, we show that the lowering operator D
u
indexed by a linear functional on polynomials u, introduced by F. Marcellán and R. Sfaxi, namely the Laguerre-Hahn derivative, is intertwining with the standard derivative D by a linear isomorphism S
u
on polynomials. This allows us to establish an intertwining relation between the nonsingular Laguerre-Hahn polynomials of
class zero of Hermite type and the Hermite polynomials, as well as some new connection formulas between such Laguerre-Hahn
polynomials and the canonical basis. 相似文献
15.
We study the problem of Hermite interpolation by polynomials in several variables. A very general definition of Hermite interpolation is adopted which consists of interpolation of consecutive chains of directional derivatives. We discuss the structure and some aspects of poisedness of the Hermite interpolation problem; using the notion of blockwise structure which we introduced in [10], we establish an interpolation formula analogous to that of Newton in one variable and use it to derive an integral remainder formula for a regular Hermite interpolation problem. For Hermite interpolation of degreen of a functionf, the remainder formula is a sum of integrals of certain (n + 1)st directional derivatives off multiplied by simplex spline functions. 相似文献
16.
Raed S. Batahan 《Linear algebra and its applications》2006,419(1):82-92
In this paper, an extension of the Hermite matrix polynomials is introduced. Some relevant matrix functions appear in terms of the two-variable Hermite matrix polynomials. Furthermore, in order to give qualitative properties of this family of matrix polynomials, the Chebyshev matrix polynomials of the second kind are introduced. 相似文献
17.
This paper describes several combinatorial models for Laguerre, Charlier, and Hermite polynomials, and uses them to prove combinatorially some classical formulas. The so-called “Italian limit formula” (from Laguerre to Hermite), the Appel identity for Hermite polynomials, and the two Sheffer identities for Laguerre and Charlier polynomials are proved. We also give bijective proofs of the three-term recurrences. These three families form the bottom triangle in R. Askey's chart classifying hypergeometric orthogonal polynomials. 相似文献
18.
Christopher S. Withers 《Journal of multivariate analysis》2010,101(9):2250-2253
We give formulas for the conditional expectations of a product of multivariate Hermite polynomials with multivariate normal arguments. These results are extended to include conditional expectations of a product of linear combination of multivariate normals. A unified approach is given that covers both Hermite and modified Hermite polynomials, as well as polynomials associated with a matrix whose eigenvalues may be both positive and negative. 相似文献
19.
本文研究了具调节因子的Hermite函数的拟谱方法在赋权Sobolev空间中函数的逼近.通过具调节因子的Hermite多项式的性质和相应的Gauss类型的求积公式,得到了在具调节因子的Hermite多项式的零点上的插值算子的稳定性以及误差界.并具有通常的高阶收敛性. 相似文献
20.
Emilio Defez 《Quaestiones Mathematicae》2018,41(2):205-212
Conventional Hermite polynomials emerge in a great diversity of applications in mathematical physics, engineering, and related fields. However, in physical systems with higher degrees of freedom it will be of practical interest to extend the scalar Hermite functions to their matrix analogue. This work introduces various new generating functions for Hermite matrix polynomials and examines existence and convergence of their associated series expansion by using Mehler’s formula for the general matrix case. Moreover, we derive interesting new relations for even- and odd-power summation in the generating-function expansion containing Hermite matrix polynomials. Some new results for the scalar case are also presented. 相似文献