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On the Positivity of Some Basic Legendre Polynomial Sums
Author(s) -
Brown Gavin,
Koumandos Stamatis,
Wang Kunyang
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799007620
Subject(s) - legendre polynomials , mathematics , legendre's equation , associated legendre polynomials , legendre function , polynomial , jacobi polynomials , classical orthogonal polynomials , pure mathematics , orthogonal polynomials , mathematical analysis , gegenbauer polynomials
The positivity of the partial sums of the series of Legendre polynomials is a classical result of Fejér. The paper presents corresponding results for both even and odd Legendre polynomials with best possible leading constants. These results have applications to demonstrating positivity of Cotes numbers at Jacobi abscissas.