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On the Zeros of the Power Series with an Application to Discontinuous Riesz-Summability

Published online by Cambridge University Press:  20 November 2018

D. Borwein  and
W. Kratz
D. Borwein
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B9
W. Kratz
Affiliation:
Department of Mathematics, The University of Western Ontario, London, Ontario, Canada N6A 5B9
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On the zeros of . If not stated otherwise, we assume throughout that κ > 0, c > 1, and that k < κ ≤ k + 1 where k = 0, 1, 2, … We reserve the symbol x to denote real numbers, and define C* = C-{x:x <-1}, C being the complex plane. Let

Information

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 19 , Issue 4 , 01 December 1976 , pp. 417 - 424
Copyright
Copyright © Canadian Mathematical Society 1976

References

1. Dieudonné, J., Foundations of modern analysis, Vol. I, Academic Press, 1969.Google Scholar
2. Kuttner, B., The high indices theorem for discontinuous Riesz means, Journal London Math. Soc. 39 (1964), 635–642.Google Scholar
3. Peyerimhoff, A., On the zeros of power series, Michigan Mathematical Journal, 13 (1966), 193–214.Google Scholar
4. Wirsing, E., On the monotonicity of the zeros of two power series, Michigan Mathematical Journal, 13 (1966), 215–218.Google Scholar