共查询到20条相似文献,搜索用时 31 毫秒
1.
María Álvarez de Morales Juan J. Moreno–Balcázar Teresa E. Pérez Miguel A. Piñar 《Acta Appl Math》2000,61(1-3):257-266
In this work, we study algebraic and analytic properties for the polynomials { Q
n
}
n 0, which are orthogonal with respect to the inner product
where , R such that – 2 > 0. 相似文献
2.
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 ,推广了著名的 Cauchy-Sheehan组合恒等式 . 相似文献
3.
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
4.
Subuhi Khan Mustafa Walid Al-Saad Ghazala Yasmin 《Applied mathematics and computation》2010,217(5):2169-2183
In this paper, the concepts and the formalism associated with monomiality principle and Sheffer sequences are used to introduce family of Hermite-based Sheffer polynomials. Some properties of Hermite-Sheffer polynomials are considered. Further, an operational formalism providing a correspondence between Sheffer and Hermite-Sheffer polynomials is developed. Furthermore, this correspondence is used to derive several new identities and results for members of Hermite-Sheffer family. 相似文献
5.
In this paper we investigate a set of orthogonal polynomials. We relate the polynomials to the Biconfluent Heun equation and present an explicit expression for the polynomials in terms of the classical Hermite polynomials. The orthogonality with a varying measure and the recurrence relation are also presented. 相似文献
6.
We establish various properties for the zero sets of three families of bivariate Hermite polynomials. Special emphasis is given to those bivariate orthogonal polynomials introduced by Hermite by means of a Rodrigues type formula related to a general positive definite quadratic form. For this family we prove that the zero set of the polynomial of total degree n+m consists of exactly n+m disjoint branches and possesses n+m asymptotes. A natural extension of the notion of interlacing is introduced and it is proved that the zero sets of the family under discussion obey this property. The results show that the properties of the zero sets, considered as affine algebraic curves in R2, are completely different for the three families analyzed. 相似文献
7.
Pankaj Mathur 《分析论及其应用》2006,22(2):105-113
In this paper, we study the explicit representation and convergence of (0, 1;0)-interpolation on infisite interval, which means to determine a polynomial of degree ≤ 3n - 2 when the function values areprescribed at two set of points namely the zeros of Hn(x) and H′n (x) and the first derivatives at the zerosof H′n(x). 相似文献
8.
The mixed moments for the Askey–Wilson polynomials are found using a bootstrapping method and connection coefficients. A similar bootstrapping idea on generating functions gives a new Askey–Wilson generating function. Modified generating functions of orthogonal polynomials are shown to generate polynomials satisfying recurrences of known degree greater than three. An important special case of this hierarchy is a polynomial which satisfies a four term recurrence, and its combinatorics is studied. 相似文献
9.
Yu. V. Kupriyanova 《Computational Mathematics and Mathematical Physics》2008,48(2):195-200
A Hermite spline of third degree is constructed on a three-dimensional simplex. The deviation of its directional derivatives up to the third order is estimated in angle-free terms. The resulting estimates hold for any tetrahedron irrespective of its geometry. 相似文献
10.
11.
We study the behavior of a class of convolution-type nonlinear transformations. Under some smallness conditions we prove the
existence of fixed points and analyze the spectrum of the associated linearized operator.
相似文献
12.
Ivá n Area Dimitar K. Dimitrov Eduardo Godoy André Ronveaux. 《Mathematics of Computation》2004,73(248):1937-1951
In this paper, sharp upper limit for the zeros of the ultraspherical polynomials are obtained via a result of Obrechkoff and certain explicit connection coefficients for these polynomials. As a consequence, sharp bounds for the zeros of the Hermite polynomials are obtained.
13.
The approximation of discrete distributions by Edgeworth expansion series for continuity points of a discrete distribution F
n implies that if t is a support point of F
n, then the expansion should be performed at a continuity point
. When a value
is selected to improve the approximation of
, and especially when a single term of the expansion is used, the selected
is defined to be a continuity correction. This paper investigates the properties of the approximations based on several terms of the expansion, when
is the value at which the infimum of a residual term is attained. Methods of selecting the estimation and the residual terms are investigated and the results are compared empirically for several discrete distributions. The results are also compared with the commonly used approximation based on the normal distribution with
. Some numerical comparisons show that the developed procedure gives better approximations than those obtained under the standard continuity correction technique, whenever
is close to 0 and 1. Thus, it is especially useful for p-value computations and for the evaluation of probabilities of rare events. 相似文献
14.
In the present paper, we establish that Riesz transforms for Dunkl Hermite expansions introduced by Nowak and Stempak are singular integral operators with Hörmander's type condition. We prove that they are bounded on Lp(Rd,dμκ) for 1<p<∞ and from L1(Rd,dμκ) into L1,∞(Rd,dμκ). 相似文献
15.
Biancamaria Della Vecchia Giuseppe Mastroianni Pter Vrtesi 《Journal of Computational and Applied Mathematics》1994,50(1-3):233-240
The authors consider a procedure of Hermite interpolation of higher order based on the zeros of Jacobi polynomials plus the endpoints ±1 and prove that such a procedure can always well approximate a function and its derivatives simultaneously in uniform norm. 相似文献
16.
F. Brackx N. De Schepper F. Sommen 《Journal of Mathematical Analysis and Applications》2008,341(1):120-130
Clifford analysis may be regarded as a higher-dimensional analogue of the theory of holomorphic functions in the complex plane. It has proven to be an appropriate framework for higher-dimensional continuous wavelet transforms, based on specific types of multi-dimensional orthogonal polynomials, such as the Clifford-Hermite polynomials, which form the building blocks for so-called Clifford-Hermite wavelets, offering a refinement of the traditional Marr wavelets. In this paper, a generalization of the Clifford-Hermite polynomials to a two-parameter family is obtained by taking the double monogenic extension of a modulated Gaussian, i.e. the classical Morlet wavelet. The eventual goal being the construction of new Clifford wavelets refining the Morlet wavelet, we first investigate the properties of the underlying polynomials. 相似文献
17.
Jagdev Singh Devendra Kumar Manish Kumar Bansal 《Mathematical Methods in the Applied Sciences》2020,43(5):2106-2116
In this paper, we find the approximate solution of a nonlinear differential equations pertaining to M-series, -function, and I-function of two variables by making use of the Hermite, Legendre, and Jacobi polynomials. The nonlinear differential equations play a key role in distinct branches of engineering and physics and many vibration problems. The results obtained in the present study are general in nature and can be used to obtain the solution of various problems of physics and engineering. 相似文献
18.
Nilay Akgnüllü Niyazi ahin Mehmet Sezer 《Numerical Methods for Partial Differential Equations》2011,27(6):1707-1721
In this study, a Hermite matrix method is presented to solve high‐order linear Fredholm integro‐differential equations with variable coefficients under the mixed conditions in terms of the Hermite polynomials. The proposed method converts the equation and its conditions to matrix equations, which correspond to a system of linear algebraic equations with unknown Hermite coefficients, by means of collocation points on a finite interval. Then, by solving the matrix equation, the Hermite coefficients and the polynomial approach are obtained. Also, examples that illustrate the pertinent features of the method are presented; the accuracy of the solutions and the error analysis are performed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 1707–1721, 2011 相似文献
19.
Shayne Waldron 《Numerical Algorithms》2007,45(1-4):231-238
The space of bivariate generalised Hermite polynomials of degree n is invariant under rotations. We exploit this symmetry to construct an orthonormal basis for which consists of the rotations of a single polynomial through the angles , ℓ=0,...n. Thus we obtain an orthogonal expansion which retains as much of the symmetry of as is possible. Indeed we show that a continuous version of this orthogonal expansion exists.
相似文献
20.
Khalfa Douak 《Journal of Computational and Applied Mathematics》1996,70(2):279-295
We are dealing with the concept of d-dimensional orthogonal (abbreviated d-orthogonal) polynomials, that is to say polynomials verifying one standard recurrence relation of order d + 1. Among the d-orthogonal polynomials one singles out the natural generalizations of certain classical orthogonal polynomials. In particular, we are concerned, in the present paper, with the solution of the following problem (P): Find all polynomial sequences which are at the same time Appell polynomials and d-orthogonal. The resulting polynomials are a natural extension of the Hermite polynomials.
A sequence of these polynomials is obtained. All the elements of its (d + 1)-order recurrence are explicitly determined. A generating function, a (d + 1)-order differential equation satisfied by each polynomial and a characterization of this sequence through a vectorial functional equation are also given. Among such polynomials one singles out the d-symmetrical ones (Definition 1.7) which are the d-orthogonal polynomials analogous to the Hermite classical ones. When d = 1 (ordinary orthogonality), we meet again the classical orthogonal polynomials of Hermite. 相似文献