Nonreal Zeros of Polynomials in a Polynomial Sequence Satisfying a Three-Term Recurrence Relation [PDF]
, 2021 This paper discusses the location of zeros of polynomials in a polynomial sequence {Pn(z)}∞n=1 generated by a three-term recurrence relation of the form Pn(z)+B(z)Pn−1(z)+A(z)Pn−k(z)=0 with k>2 and the standard initial conditions P0(z)=1, P−1(z)=P−k+1(
Ndikubwayo, Innocent,
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Quasi-orthogonality and real zeros of some 2F2 and 3F2 polynomials [PDF]
, 2015 In this paper, we prove the quasi-orthogonality of a family of 2F2 polynomials and several classes of 3F2 polynomials that do not appear in the Askey scheme for hypergeometric orthogonal polynomials.
Johnston, S.J., Jordaan, Kerstin Heidrun
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Asymptotically extremal polynomials with respect to varying weights and application to Sobolev orthogonality [PDF]
, 2008 9 pages, no figures.-- MSC2000 code: 33C45.MR#: MR2431543 (2009g:41009)Zbl#: Zbl 1155.33006We study the asymptotic behavior of the zeros of a sequence of polynomials whose weighted norms, with respect to a sequence of weight functions, have the same $n ...
Díaz Mendoza, Carlos J. +3 more
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Location of Zeros of Chromatic and Related Polynomials of Graphs [PDF]
, 1994 We consider the location of zeros of four related classes of polynomials, one of which is the class of chromatic polynomials of graphs. All of these polynomials are generating functions of combinatorial interest.
David G. Wagner +2 more
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Zeros of 3F2 hypergeometric polynomials [PDF]
, 2001 We investigate the behaviour of the zeros of three distinct types of 3F2 hypergeometric polynomials. Each type of polynomial considered has degree 2n and contains a free parameter b.
Driver, K.A. +3 more
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Zeros of expansions in orthogonal polynomials [PDF]
, 1989 The theory of bi-orthogonal polynomials is exploited to investigate the location of zeros of truncated expansions in orthogonal polynomials. It turns out that, subject to additional conditions, these zeros can be confined to certain real intervals.
A. Iserles, E. B. Saff
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Location of the zeros of polynomials satisfying three-term recurrence relations. III. Positive coefficients case [PDF]
, 1985 The location of the zeros of a family of polynomials satisfying a three-term recurrence relation are studied. Various cases where some of the coefficients are positive or merely real (but the main coefficients are positive) are considered, and new ...
Leopold, E
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Zeros of Sobolev Orthogonal Polynomials of Gegenbauer Type [PDF]
, 2002 Let {Sn}n denote the monic orthogonal polynomial sequence with respect to the Sobolev inner product〈f, g〉S=∫f(x)g(x)dψ0 (x)+λ∫f(x)g(x)dψ1 (x), where λ>0 and {dψ0, dψ1} is a so-called symmetrically coherent pair, with dψ0 or dψ1 the classical Gegenbauer ...
Groenevelt, W.G.M.
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On the zeros of complex Van Vleck polynomials [PDF]
, 2009 Polynomial solutions to the generalized Lamé equation, the Stieltjes polynomials, and the associated Van Vleck polynomials, have been studied extensively in the case of real number parameters. In the complex case, relatively little is known.
Bourget, A., Agnew, A., McMillen, T.
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Continuation methods for the computation of zeros of Szegö polynomials [PDF]
, 1996 Let {φj}∞j = 0 be a family of monic polynomials that are orthogonal with respect to an inner product on the unit circle. The polynomials φj arise in time series analysis and are often referred to as Szegö polynomials or Levinson polynomials.
Reichel, L., Ammar, G.S., Calvetti, D.
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