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Proof of a Conjecture of Schoenberg on the Generating Function of a Totally Positive Sequence

Published online by Cambridge University Press:  20 November 2018

Albert Edrei
Albert Edrei*
Affiliation:
Syracuse University
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Let

be a sequence of real terms with which we associate the generating power series

We consider the following definition due to Schoenberg [7, p. 362]:

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 5 , 1953 , pp. 86 - 94
Copyright
Copyright © Canadian Mathematical Society 1953

References

1. Aissen, M., Schoenberg, I. J., and Whitney, A., On the generating functions of totally positive sequences I, Journal d'Analyse Mathématique, not yet published. Google Scholar
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3. Edrei, A., On the generating functions of totally positive sequences II, Journal d'Analyse Mathématique, not yet published. Google Scholar
4. Nevanlinna, R., Le théorème de Picard-Borel et la théorie des fonctions méromorphes (Paris, 1929).Google Scholar
5. Perron, O., Die Lehre von den Kettenbrüchen, 2nd ed. (Leipzig, 1929).Google Scholar
6. Schoenberg, I. J., Zur Abzählung der reellen Wurzeln algebraischer Gleichungent, Math. Z., 38 (1934), 546–564.Google Scholar
7. Schoenberg, I. J. Some analytical aspects of the problem of smoothing, Courant Anniversary Volume (New York, 1948), 351–369.Google Scholar
8. Whitney, A., A reduction theorem for totally positive matrices, Journal d'Analyse Mathématique, not yet published.Google Scholar