Jacobi series for general parameters via Hadamard finite part and application to nonhomogeneous hypergeometric equations

DOI10.1155/2019/2473212zbMath1486.33012OpenAlexW2946243782WikidataQ127794447 ScholiaQ127794447MaRDI QIDQ2330271

Rodica D. Costin, Marina David

Publication date: 28 October 2019

Published in: International Journal of Mathematics and Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2019/2473212

zbMATH Keywords

Jacobi polynomialsanalytic functionsHadamard principal part

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Other functions coming from differential, difference and integral equations (33E30) Singularities, monodromy and local behavior of solutions to ordinary differential equations in the complex domain, normal forms (34M35)

Uses Software

• DLMF

Cites Work

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• Riemann--Hilbert analysis for Jacobi polynomials orthogonal on a single contour
• NIST digital library of mathematical functions
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• Orthogonality of Jacobi and Laguerre polynomials for general parameters via the Hadamard finite part
• A proof for the mode stability of a self-similar wave map
• Nonlinear perturbations of Fuchsian systems: corrections and linearization, normal forms
• Analytic linearization of nonlinear perturbations of Fuchsian systems
• Expansion of Analytic Functions in Jacobi Series
• Distributional Weight Functions for Orthogonal Polynomials
• Nonintegrability criteria for a class of differential equations with two regular singular points

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