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ON THE POSITIVITY OF SOME BASIC LEGENDRE POLYNOMIAL SUMS

Published online by Cambridge University Press:  01 June 1999

GAVIN BROWN ,
STAMATIS KOUMANDOS  and
KUNYANG WANG
GAVIN BROWN
Affiliation:
University of Sydney, Sydney, NSW 2006, Australia
STAMATIS KOUMANDOS
Affiliation:
Department of Mathematics and Statistics, University of Cyprus, PO Box 537, 1678 Nicosia, Cyprus
KUNYANG WANG
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, China
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Abstract

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.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 59 , Issue 3 , June 1999 , pp. 939 - 954
Copyright
The London Mathematical Society 1999

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