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Positivity of more Jacobi polynomial sums

Published online by Cambridge University Press:  24 October 2008

Gavin Brown ,
Stamatis Koumandos  and
Kun-Yang Wang
Gavin Brown
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide 5005, South Australia
Stamatis Koumandos
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide 5005, South Australia
Kun-Yang Wang
Affiliation:
Department of Mathematics, Beijing Normal University, Beijing 100875, China
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Extract

Our main result can be stated as follows:

Theorem.

for all λ ≥ λ0, where λ0 is the unique root in (0, 1) of the equation

andis the Gegenbauer polynomial of degree 2k and order λ. The only cases of equality in (1·1) are when θ = 0 and n is odd.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 4 , May 1996 , pp. 681 - 694
Copyright
Copyright © Cambridge Philosophical Society 1996

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References

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