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Cyclically Ordered Sets

Published online by Cambridge University Press:  20 November 2018

M. I. Aissen
M. I. Aissen*
Affiliation:
Johns Hopkins University
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The classical separation theorems regarding the relative position of the zeros of two consecutive orthogonal polynomials, or of the positive zeros of two consecutive Bessel Functions, are well known. Less well known is a theorem of Bôcher and Porter (1, p. 237), which states that the positive zeros of three consecutive Bessel Functions occur in cyclic order.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 9 , 1957 , pp. 406 - 412
Copyright
Copyright © Canadian Mathematical Society 1957

References

1. Bôcher, Maxime, On certain methods of Sturm and their applications to the roots of Bessel's functions, Bull. Amer. Math. Soc, 3 (1897), 205–213.Google Scholar
2. Edrei, Albert, Proof of a conjecture of Schoenberg on the generating function of a totally positive sequence, Can. J. Math., 5 (1953), 86–94.Google Scholar
3. Schoenberg, I. J., Some analytic aspects of the problem of smoothing, Studies and Essays Presented to R. Courant on his 60th Birthday (New York, 1948), 351–369.Google Scholar
4. Szegö, Gabor, Orthogonal polynomials, Amer. Math. Soc. Coll. Publ. 23 (New York, 1939), 41.Google Scholar