New inequalities from classical Sturm theorems

DOI10.1016/j.jat.2004.09.006zbMath1065.33004OpenAlexW2011742520MaRDI QIDQ707205

Javier Segura, Alfredo Deaño, Amparo Gil

Publication date: 9 February 2005

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/10016/6647

zbMATH Keywords

orthogonal polynomialshypergeometric functionsSturn comparison theorem

Mathematics Subject Classification ID

Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Other analytical inequalities (26D20) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15)

Related Items (9)

Zeros of orthogonal polynomials near an algebraic singularity of the measure ⋮ Orthogonality and asymptotics of pseudo-Jacobi polynomials for non-classical parameters ⋮ The Schwarzian-Newton method for solving nonlinear equations, with applications ⋮ Global Sturm inequalities for the real zeros of the solutions of the Gauss hypergeometric differential equation ⋮ Zeros of Orthogonal Polynomials ⋮ Fast and reliable high-accuracy computation of Gauss-Jacobi quadrature ⋮ Interlacing of the zeros of contiguous hypergeometric functions ⋮ Convexity of the zeros of some orthogonal polynomials and related functions ⋮ Fast, reliable and unrestricted iterative computation of Gauss-Hermite and Gauss-Laguerre quadratures

Cites Work

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• Uniform asymptotics for the incomplete gamma functions starting from negative values of the parameters
• A property of the zeros of the Legendre polynomials
• On the zeros and turning points of special functions.
• On a conjecture regarding the extrema of Bessel functions and its generalization
• Computing the real zeros of hypergeometric functions
• Some Consequences of the Sturm Comparison Theorem
• On the Spacing of the Zeros of Some Classical Orthogonal Polynomials
• Computing the Zeros and Turning Points of Solutions of Second Order Homogeneous Linear ODEs
• The Zeros of Special Functions from a Fixed Point Method

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