共查询到20条相似文献,搜索用时 11 毫秒
1.
We show that the zeros of the hypergeometric polynomials
,
, cluster on the loop of the lemniscate
as
. We also state the equations of the curves on which the zeros of
, lie asymptotically as
. Auxiliary results for the asymptotic zero distribution of other functions related to hypergeometric polynomials are proved,
including Jacobi polynomials with varying parameters and associated Legendre functions. Graphical evidence is provided using
Mathematica.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
2.
G. Lpez Lagomasino I. Prez Izquierdo H. Pijeira Cabrera 《Journal of Approximation Theory》2005,137(2):2225-237
We study the zero location and asymptotic zero distribution of sequences of polynomials which satisfy an extremal condition with respect to a norm given on the space of all polynomials. 相似文献
3.
Wolfgang Erb 《Applied mathematics and computation》2011,217(9):4771-4780
We investigate monotonicity properties of extremal zeros of orthogonal polynomials depending on a parameter. Using a functional analysis method we prove the monotonicity of extreme zeros of associated Jacobi, associated Gegenbauer and q-Meixner-Pollaczek polynomials. We show how these results can be applied to prove interlacing of zeros of orthogonal polynomials with shifted parameters and to determine optimally localized polynomials on the unit ball. 相似文献
4.
5.
6.
Mark V. DeFazio Martin E. Muldoon 《Journal of Mathematical Analysis and Applications》2007,334(2):977-982
For each the nth Laguerre polynomial has an m-fold zero at the origin when α=−m. As the real variable α→−m, it has m simple complex zeros which approach 0 in a symmetric way. This symmetry leads to a finite value for the limit of the sum of the reciprocals of these zeros. There is a similar property for the zeros of the q-Laguerre polynomials and of the Jacobi polynomials and similar results hold for sums of other negative integer powers. 相似文献
7.
Chelo Ferreira Jos L. Lpez Ester Prez Sinusía 《Journal of Computational and Applied Mathematics》2008,217(1):88-109
It has been shown in Ferreira et al. [Asymptotic relations in the Askey scheme for hypergeometric orthogonal polynomials, Adv. in Appl. Math. 31(1) (2003) 61–85], López and Temme [Approximations of orthogonal polynomials in terms of Hermite polynomials, Methods Appl. Anal. 6 (1999) 131–146; The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis, J. Comput. Appl. Math. 133 (2001) 623–633] that the three lower levels of the Askey table of hypergeometric orthogonal polynomials are connected by means of asymptotic relations. In Ferreira et al. [Limit relations between the Hahn polynomials and the Hermite, Laguerre and Charlier polynomials, submitted for publication] we have established new asymptotic connections between the fourth level and the two lower levels. In this paper, we continue with that program and obtain asymptotic expansions between the fourth level and the third level: we derive 16 asymptotic expansions of the Hahn, dual Hahn, continuous Hahn and continuous dual Hahn polynomials in terms of Meixner–Pollaczek, Jacobi, Meixner and Krawtchouk polynomials. From these expansions, we also derive three new limits between those polynomials. Some numerical experiments show the accuracy of the approximations and, in particular, the accuracy in the approximation of the zeros of those polynomials. 相似文献
8.
In this paper we extend a classical result due to Cauchy and its improvement due to Datt and Govil to a class of lacunary
type polynomials. 相似文献
9.
N. Ben Romdhane 《Journal of Mathematical Analysis and Applications》2008,344(2):888-897
In this paper, we give some properties of the zeros of d-symmetric d-orthogonal polynomials and we localize these zeros on (d+1) rays emanating from the origin. We apply the obtained results to some known polynomials. In particular, we partially solve the conjecture about the zeros of the Humbert polynomials stated by Milovanovi? and Dordevi? [G.V. Milovanovi?, G.B. Dordevi?, On some properties of Humbert's polynomials, II, Ser. Math. Inform. 6 (1991) 23-30]. A study of the eigenvalues of a particular banded Hessenberg matrix is done. 相似文献
10.
We study the asymptotic behavior of the zeros of certain families of 3F2 functions. Classical tools are used to analyse the asymptotic behavior of the zeros of the polynomial
In addition, families of 3F2 functions that are connected in a formulaic sense with Gauss hypergeometric polynomials of the form
and
are investigated. Numerical evidence of the clustering o zeros on certain curves is generated by Mathematica. 相似文献
11.
In this paper, we treat three questions related to the d-orthogonality of the Humbert polynomials. The first one consists to determinate the explicit expression of the d-dimensional functional vector for which the d-orthogonality holds. The second one is the investigation of the components of Humbert polynomial sequence. That allows us to introduce, as far as we know, new d-orthogonal polynomials generalizing the classical Jacobi ones. The third one consists to solve a characterization problem related to a generalized hypergeometric representation of the Humbert polynomials. 相似文献
12.
Hanan Aljubran Maxim L. Yattselev 《Journal of Mathematical Analysis and Applications》2019,469(1):428-446
Let be a sequence of orthonormal polynomials on the unit circle with respect to a positive Borel measure μ that is symmetric with respect to conjugation. We study asymptotic behavior of the expected number of real zeros, say , of random polynomials where are i.i.d. standard Gaussian random variables. When μ is the acrlength measure such polynomials are called Kac polynomials and it was shown by Wilkins that admits an asymptotic expansion of the form (Kac himself obtained the leading term of this expansion). In this work we generalize the result of Wilkins to the case where μ is absolutely continuous with respect to arclength measure and its Radon–Nikodym derivative extends to a holomorphic non-vanishing function in some neighborhood of the unit circle. In this case admits an analogous expansion with the coefficients depending on the measure μ for (the leading order term and remain the same). 相似文献
13.
Let , with
-1=x0n<x1n<<xnn<xn+1,n=1