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A Lower Bound for the Number of Negative Zeros of Power Series

Published online by Cambridge University Press:  20 November 2018

W. Gawronski
W. Gawronski*
Affiliation:
Abteilung für Mathematik Universität Ulm Oberer EselbergD7900 Ulm/DonauGermany
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In this paper we are concerned with power series of the type

1

which admit unique analytic extension onto a domain containing the negative real axis. Our primary object is to establish a general theorem giving a lower estimate for the number of different zeros of (1) on the negative real axis. W. Jurkat and A. Peyerimhoff showed that for a certain class of coefficient functions a(z) the number of negative zeros of (1) is closely related to the behaviour of a(z) at z = 0. In particular they proved the following theorem [4, p. 219, Theorem 4].

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 22 , Issue 1 , 01 March 1979 , pp. 47 - 52
Copyright
Copyright © Canadian Mathematical Society 1979

References

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