共查询到20条相似文献,搜索用时 0 毫秒
1.
In the present paper we deal with the polynomials Ln(α,M,N) (x) orthogonal with respect to the Sobolev inner product
2.
Cem Kaano?lu 《Journal of Computational and Applied Mathematics》2011,235(16):4878-4887
The purpose of this paper is to introduce and discuss a more general class of multiple Hermite polynomials. In this work, the explicit forms, operational formulas and a recurrence relation are obtained. Furthermore, we derive several families of bilinear, bilateral and mixed multilateral finite series relationships and generating functions for the generalized multiple Hermite polynomials. 相似文献
3.
We study interlacing properties of the zeros of two types of linear combinations of Laguerre polynomials with different parameters, namely and . Proofs and numerical counterexamples are given in situations where the zeros of Rn, and Sn, respectively, interlace (or do not in general) with the zeros of , , k=n or n−1. The results we prove hold for continuous, as well as integral, shifts of the parameter α. 相似文献
4.
R. Gow has investigated the problem of determining classical polynomials with Galois group Am, the alternating group on m letters, in the case that m is even (odd m being previously handled in work of I. Schur). He showed that the generalized Laguerre polynomial Lm(m)(x), defined below, has Galois group Am provided m>2 is even and Lm(m)(x) is irreducible (and obtained irreducibility in some cases). In this paper, we establish that Lm(m)(x) is irreducible for almost all m (and, hence, has Galois group Am for almost all even m). 相似文献
5.
6.
7.
8.
The goal of this work is to characterize all second order difference operators of several variables that have discrete orthogonal polynomials as eigenfunctions. Under some mild assumptions, we give a complete solution of the problem. 相似文献
9.
Diego Dominici 《Journal of Computational and Applied Mathematics》2010,233(6):1511-1518
Following the lead of J. Dehesa and his collaborators, we compute the Fisher information of the Meixner-Pollaczek, Meixner, Krawtchouk and Charlier polynomials. 相似文献
10.
11.
Nathan Kaplan 《Journal of Number Theory》2007,127(1):118-126
We say that a cyclotomic polynomial Φn has order three if n is the product of three distinct primes, p<q<r. Let A(n) be the largest absolute value of a coefficient of Φn. For each pair of primes p<q, we give an infinite family of r such that A(pqr)=1. We also prove that A(pqr)=A(pqs) whenever s>q is a prime congruent to . 相似文献
12.
Generalized permutahedra are the polytopes obtained from the permutahedron by changing the edge lengths while preserving the edge directions, possibly identifying vertices along the way. We introduce a “lifting” construction for these polytopes, which turns an n -dimensional generalized permutahedron into an (n+1)-dimensional one. We prove that this construction gives rise to Stasheff ?s multiplihedron from homotopy theory, and to the more general “nestomultiplihedra”, answering two questions of Devadoss and Forcey. 相似文献
13.
Gennady Bachman 《Journal of Number Theory》2003,100(1):104-116
We study coefficients of ternary cyclotomic polynomials Φpqr(z)=∏ρ(z−ρ), where p, q, and r are distinct odd primes and the product is taken over all primitive pqrth roots of unity ρ. 相似文献
14.
《Mathematische Nachrichten》2017,290(11-12):1716-1731
Exceptional orthogonal Laguerre polynomials can be viewed as an extension of the classical Laguerre polynomials per excluding polynomials of certain order(s) from being eigenfunctions for the corresponding exceptional differential operator. We are interested in the (so‐called) Type I X1‐Laguerre polynomial sequence , and , where the constant polynomial is omitted. We derive two representations for the polynomials in terms of moments by using determinants. The first representation in terms of the canonical moments is rather cumbersome. We introduce adjusted moments and find a second, more elegant formula. We deduce a recursion formula for the moments and the adjusted ones. The adjusted moments are also expressed via a generating function. We observe a certain detachedness of the first two moments from the others. 相似文献
15.
We study convexity properties of the zeros of some special functions that follow from the convexity theorem of Sturm. We prove results on the intervals of convexity for the zeros of Laguerre, Jacobi and ultraspherical polynomials, as well as functions related to them, using transformations under which the zeros remain unchanged. We give upper as well as lower bounds for the distance between consecutive zeros in several cases. 相似文献
16.
17.
H. T. Koelink 《Acta Appl Math》1996,44(3):295-352
Generalised matrix elements of the irreducible representations of the quantum SU(2) group are defined using certain orthonormal bases of the representation space. The generalised matrix elements are relatively infinitesimal invariant with respect to Lie algebra like elements of the quantised universal enveloping algebra of sl(2). A full proof of the theorem announced by Noumi and Mimachi [Proc. Japan Acad. Sci. Ser. A
66 (1990), 146–149] describing the generalised matrix elements in terms of the full four-parameter family of Askey-Wilson polynomials is given. Various known and new applications of this interpretation are presented.Supported by a NATO-Science Fellowship of the Netherlands Organization for Scientific Research (NWO). 相似文献
18.
Shaofang Hong 《Linear algebra and its applications》2008,428(4):1001-1008
Let a,b and n be positive integers and the set S={x1,…,xn} of n distinct positive integers be a divisor chain (i.e. there exists a permutation σ on {1,…,n} such that xσ(1)|…|xσ(n)). In this paper, we show that if a|b, then the ath power GCD matrix (Sa) having the ath power (xi,xj)a of the greatest common divisor of xi and xj as its i,j-entry divides the bth power GCD matrix (Sb) in the ring Mn(Z) of n×n matrices over integers. We show also that if a?b and n?2, then the ath power GCD matrix (Sa) does not divide the bth power GCD matrix (Sb) in the ring Mn(Z). Similar results are also established for the power LCM matrices. 相似文献
19.
R.B. Paris 《Journal of Computational and Applied Mathematics》2009,232(2):216-226
The Hermite-Bell polynomials are defined by for n=0,1,2,… and integer r≥2 and generalise the classical Hermite polynomials corresponding to r=2. We obtain an asymptotic expansion for as n→∞ using the method of steepest descents. For a certain value of x, two saddle points coalesce and a uniform approximation in terms of Airy functions is given to cover this situation. An asymptotic approximation for the largest positive zeros of is derived as n→∞. Numerical results are presented to illustrate the accuracy of the various expansions. 相似文献
20.
Rabia Akta? Abdullah Alt?n Fatma Ta?delen 《Journal of Computational and Applied Mathematics》2011,235(16):4825-4833
The main object of this paper is to construct a two-variable analogue of Jacobi polynomials and to give some properties of these polynomials. We show that these polynomials are orthogonal, then we obtain various recurrence formulas for them. Furthermore, we give some integral representations for these polynomials. 相似文献