Positivity of certain sums over Jacobi kernel polynomials

DOI10.1016/J.AAM.2007.12.001zbMath1173.33009OpenAlexW2031686193MaRDI QIDQ950413

Veronika Pillwein

Publication date: 22 October 2008

Published in: Advances in Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aam.2007.12.001

zbMATH Keywords

Chebyshev polynomialsJacobi polynomialskernel polynomialsultraspherical polynomialspositive sums

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (4)

Closed form solutions of linear difference equations in terms of symmetric products ⋮ On the positivity of the Gillis-Reznick-Zeilberger rational function ⋮ A comparison of algorithms for proving positivity of linearly recurrent sequences ⋮ A hypergeometric inequality

Uses Software

• Mathematica
• SumCracker
• GeneratingFunctions

Cites Work

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• SumCracker: A package for manipulating symbolic sums and related objects
• The kernel polynomial method
• Positive Jacobi Polynomial Sums, II
• Positive Sums of the Classical Orthogonal Polynomials
• A procedure for proving special function inequalities involving a discrete parameter
• A posteriori error estimates for Maxwell equations

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