Jacobi series for general parameters via Hadamard finite part and application to nonhomogeneous hypergeometric equations
type: Item
instance of: scholarly article
title: Jacobi series for general parameters via Hadamard finite part and application to nonhomogeneous hypergeometric equations
zbMATH Open document ID: 1486.33012
DOI: 10.1155/2019/2473212
author: R. D. Costin
author: Marina David
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2019-10-28T00:00:00Z
review text: Summary: The representation of analytic functions as convergent series in Jacobi polynomials \(P_n^{(\alpha, \beta)}\) is reformulated using the Hadamard principal part of integrals for all \(\alpha\), \(\beta\in\mathbb{C}\backslash \{0,-1,-2,\dots\}\), \(\alpha + \beta\neq -2,-3,\dots\). The coefficients of the series are given as usual integrals in the classical case (when \(\mathfrak{R} \alpha, \mathfrak{R} \beta > - 1)\) or by their Hadamard principal part when they diverge. As an application it is shown that nonhomogeneous differential equations of hypergeometric type do generically have a unique solution which is analytic at both singular points in \(\mathbb{C}\).
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 34M35
Mathematics Subject Classification ID: 33E30
zbMATH DE Number: 7122630
zbMATH Keywords: analytic functions
zbMATH Keywords: Jacobi polynomials
zbMATH Keywords: Hadamard principal part
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2019/2473212
OpenAlex ID: W2946243782
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Wikidata QID: Q127794447
describes a project that uses: Digital Library of Mathematical Functions
description: scientific article