On the positivity of some basic Legendre polynomial sums

Authors
Brown, G Koumandos, S Wang, KY
Citation
G. Brown et al., On the positivity of some basic Legendre polynomial sums, J LOND MATH, 59, 1999, pp. 939-954
Citations number
19
Categorie Soggetti
Mathematics
Journal title
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES
ISSN journal
00246107 → ACNP
Volume
59
Year of publication
1999
Part
3
Pages
939 - 954
Database
ISI
SICI code
0024-6107(199906)59:<939:OTPOSB>2.0.ZU;2-D
Abstract
The positivity of the partial sums of the series of Legendre polynomials is a classical result of Fejer. 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 numb ers at Jacobi abscissas.