共查询到10条相似文献,搜索用时 62 毫秒
1.
In this paper, the multi-variable Hermite matrix polynomials are introduced by algebraic decomposition of exponential operators. Their properties are established using operational methods. The matrix forms of the Chebyshev and truncated polynomials of two variable are also introduced, which are further used to derive certain operational representations and expansion formulae. 相似文献
2.
R. S. Batahan 《分析论及其应用》2013,29(2):97-103
The primary purpose of this paper is to present the Volterra integral equation of the two-variable Hermite matrix polynomials. Moreover, a new representation of these matrix polynomials are established here. 相似文献
3.
Bojan Orel 《Journal of Computational and Applied Mathematics》2012,236(7):1753-1765
An efficient construction of two non-classical families of orthogonal polynomials is presented in the paper. The so-called half-range Chebyshev polynomials of the first and second kinds were first introduced by Huybrechs in Huybrechs (2010) [5]. Some properties of these polynomials are also shown. Every integrable function can be represented as an infinite series of sines and cosines of these polynomials, the so-called half-range Chebyshev-Fourier (HCF) series. The second part of the paper is devoted to the efficient computation of derivatives and multiplication of the truncated HCF series, where two matrices are constructed for this purpose: the differentiation and the multiplication matrix. 相似文献
4.
A class of generalized complex polynomials of Hermite type, suggested by a special magnetic Schrödinger operator, is introduced and some related basic properties are discussed. 相似文献
5.
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
6.
Emilio Defez 《Applied Mathematics Letters》2013,26(8):899-903
This paper centers on the derivation of a Rodrigues-type formula for the Gegenbauer matrix polynomial. A connection between Gegenbauer and Jacobi matrix polynomials is given. 相似文献
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8.
Let Hn be the nth Hermite polynomial, i.e., the nth orthogonal on
polynomial with respect to the weight w(x)=exp(−x2). We prove the following: If f is an arbitrary polynomial of degree at most n, such that |f||Hn| at the zeros of Hn+1, then for k=1,…,n we have f(k)Hn(k), where · is the
norm. This result can be viewed as an inequality of the Duffin and Schaeffer type. As corollaries, we obtain a Markov-type inequality in the
norm, and estimates for the expansion coefficients in the basis of Hermite polynomials. 相似文献
9.
Johann Cigler 《Journal of Combinatorial Theory, Series A》2011,118(1):9-26
Two well-known q-Hermite polynomials are the continuous and discrete q-Hermite polynomials. In this paper we consider a new family of q-Hermite polynomials and prove several curious properties about these polynomials. One striking property is the connection with q-Fibonacci and q-Lucas polynomials. The latter relation yields a generalization of the Touchard-Riordan formula. 相似文献
10.
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