Refined estimates on the growth rate of Jacobi polynomials

Izen, Steven H.

doi:10.1016/j.jat.2006.04.007

Cited by 4 publications

(1 citation statement)

References 7 publications

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“…Gawronski and Shawyer [49] used (31) to calculate the asymptotic distribution of the zeros of the Jacobi polynomials P (α+an,β+bn) n (x) as n → ∞. Many other developments, which have emerged essentially from the Srivastava-Singhal generating functions ( 27), ( 29) and (31), include those presented in (for example) [42,50,51] and also in [52][53][54].…”

Section: Generating Functions Of Orthogonal Polynomialsmentioning

confidence: 99%

Some Families of Generating Functions Associated with Orthogonal Polynomials and Other Higher Transcendental Functions

Srivástava

2022

Mathematics

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In this invited survey-cum-expository review article, we present a brief and comprehensive account of some general families of linear and bilinear generating functions which are associated with orthogonal polynomials and such other higher transcendental functions as (for example) hypergeometric functions and hypergeometric polynomials in one, two and more variables. Many of the results as well as the methods and techniques used for their derivations, which are presented here, are intended to provide incentive and motivation for further research on the subject investigated in this article.

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Section: Generating Functions Of Orthogonal Polynomialsmentioning

confidence: 99%

Some Families of Generating Functions Associated with Orthogonal Polynomials and Other Higher Transcendental Functions

Srivástava

2022

Mathematics

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A finitization of the bead process

Fleming

Forrester

Nordenstam

2010

Probab. Theory Relat. Fields

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Abstract. The bead process is the particle system defined on parallel lines, with underlying measure giving constant weight to all configurations in which particles on neighbouring lines interlace, and zero weight otherwise. Motivated by the statistical mechanical model of the tiling of an abc-hexagon by three species of rhombi, a finitized version of the bead process is defined. The corresponding joint distribution can be realized as an eigenvalue probability density function for a sequence of random matrices. The finitized bead process is determinantal, and we give the correlation kernel in terms of Jacobi polynomials. Two scaling limits are considered: a global limit in which the spacing between lines goes to zero, and a certain bulk scaling limit. In the global limit the shape of the support of the particles is determined, while in the bulk scaling limit the bead process kernel of Boutillier is reclaimed, after approriate identification of the anisotropy parameter therein.

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On the asymptotic behavior of Jacobi polynomials with first varying parameter

Szehr

Zarouf

2022

Journal of Approximation Theory

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Refined estimates on the growth rate of Jacobi polynomials

Cited by 4 publications

References 7 publications

Some Families of Generating Functions Associated with Orthogonal Polynomials and Other Higher Transcendental Functions

Some Families of Generating Functions Associated with Orthogonal Polynomials and Other Higher Transcendental Functions

A finitization of the bead process

On the asymptotic behavior of Jacobi polynomials with first varying parameter

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