Abstract
THE problem of generalizing the following basic identity 
given in Hardy, Littlewood and Pólya1, remains to be considered. We shall show that the generalized Cauchy inequality follows immediately from this generalization. The resulting identity has many fruitful applications in problems of multivariate ratio estimation in sample survey theory.
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References
Hardy, G. H., Littlewood, J. E., and Pólya, G., in Inequalities (Cambridge University Press, 1934).
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KOOP, J., GRAY, G. Identity for the Product of Two Positive Definite Quadratic Forms. Nature 216, 304 (1967). https://doi.org/10.1038/216304a0
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DOI: https://doi.org/10.1038/216304a0
