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Two inequalities for the complete symmetric functions

Published online by Cambridge University Press:  24 October 2008

V. J. Baston
V. J. Baston
Affiliation:
University of Southampton
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Extract

In (l) Hunter proved that the complete symmetric functions of even order are positive definite by obtaining the inequality

where ht denotes the complete symmetric function of order t. In this note we show that the inequality can be strengthened, which, in turn, enables theorem 2 of (l) to be sharpened. We also obtain a special case of an inequality conjectured by McLeod(2).

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 84 , Issue 1 , July 1978 , pp. 1 - 3
Copyright
Copyright © Cambridge Philosophical Society 1978

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References

REFERENCES

(1)Hunter, D. B.The positive-definiteness of the complete symmetric functions of even order. Math. Proc. Cambridge Philos. Soc. 82 (1977), 255–258.Google Scholar
(2)McLeod, J. B.On four inequalities in symmetric functions. Proc. Edinburgh Math. Soc. 11 (1959), 305–312.Google Scholar
(3)Mitrinovic, D. S.Analytic inequalities (Springer-Verlag, 1970).Google Scholar