On Turán's inequality for Legendre polynomials

DOI10.1016/j.exmath.2006.11.001zbMath1155.26012OpenAlexW2153193647MaRDI QIDQ996999

Stefan Gerhold, Horst Alzer, Manuel Kauers, Alexandru Lupaş

Publication date: 19 July 2007

Published in: Expositiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.exmath.2006.11.001

zbMATH Keywords

Legendre polynomialsTurán's inequality

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Inequalities for trigonometric functions and polynomials (26D05)

Related Items (12)

Differential equation and inequalities of the generalized \(\mathtt{k}\)-Bessel functions ⋮ Some properties of a hypergeometric function which appear in an approximation problem ⋮ Turán type inequalities for Tricomi confluent hypergeometric functions ⋮ Turán type inequalities for hypergeometric functions ⋮ Functional inequalities involving Bessel and modified Bessel functions of the first kind ⋮ On the positivity of the Gillis-Reznick-Zeilberger rational function ⋮ TURÁN TYPE INEQUALITIES FOR MODIFIED BESSEL FUNCTIONS ⋮ A refinement of Vietoris' inequality for sine polynomials ⋮ Turán's inequality, nonnegative linearization and amenability properties for associated symmetric Pollaczek polynomials ⋮ Difference Equation Theory Meets Mathematical Finance ⋮ Bounds on Turán determinants ⋮ A hypergeometric inequality

Uses Software

• Mathematica
• SumCracker

Cites Work

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• No two quotients of normalized binomial mid-coefficients are equal
• Liouville's operator for a disc in space
• Dedication: Remembering Paul Turán
• The special functions and their approximations. Vol. I, II
• Normalized binomial mid-coefficients and power means
• Positivity of Tur\'an determinants for orthogonal polynomials
• Higher order Turán inequalities
• A procedure for proving special function inequalities involving a discrete parameter
• An Inequality of Turan Type for Jacobi Polynomials

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