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The positive-definiteness of the complete symmetric functions of even order

Published online by Cambridge University Press:  24 October 2008

D. B. Hunter
D. B. Hunter
Affiliation:
University of Bradford
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Extract

An important role in the classical theory of symmetric functions of a real n-tuple x = (x1, x2, …, xn) is played by the complete symmetric functions or homogeneous product sums hr defined by the generating function

(see Littlewood (5), p. 82). In an earlier paper (4) I conjectured that h2r is positive definite. The main object of the present paper is to prove this conjecture in a rather sharper form.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 82 , Issue 2 , September 1977 , pp. 255 - 258
Copyright
Copyright © Cambridge Philosophical Society 1977

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References

REFERENCES

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