Positivity of Cotes numbers at more Jacobi abscissas
type: Item
instance of: scholarly article
title: Positivity of Cotes numbers at more Jacobi abscissas
zbMATH Open document ID: 0860.33005
DOI: 10.1007/BF01298452
author: Gavin Brown
author: Stamatis Koumandos
author: Wang Kunyang
published in: Monatshefte für Mathematik
publication date: 1996-08-27T00:00:00Z
full work available at URL: https://eudml.org/doc/178734
review text: Let \(P_n^{(\alpha, \beta)} (x)\) the \(n\)-th Jacobi polynomial and consider the expansion \[ (1-x)^{-\gamma} (1+x)^{-d}\sim \sum^\infty_{k=0} a_k P_n^{(\alpha, \beta)}(x). \] The authors study the positivity of the partial sums \(S_n= \sum^n_{k=0} a_k P_n^{(\alpha, \beta)}(x)\), \(-1\leq x\leq 1\), \(n=0, 1,\dots\), and establish some new cases of positivity of such sums.
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 33C20
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 42C10
zbMATH DE Number: 920727
zbMATH Keywords: positivity of Cotes numbers
zbMATH Keywords: Jacobi polynomial
reviewed by: Luigi Gatteschi
MaRDI profile type: Publication
cites work: Positivity of the Cotes numbers for some Jacobi abscissas
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description: scientific article; zbMATH DE number 920727