Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-21T07:49:41.157Z Has data issue: false hasContentIssue false

On the Zeros of Power Series with Exponential Logarithmic Coefficients

Published online by Cambridge University Press:  20 November 2018

W. Gawronski
Affiliation:
Abteilung für MathematikUniversität UlmOberer Eselsberg D-7900 ULM, Germany
U. Stadtmüller
Affiliation:
Abteilung für MathematikUniversität UlmOberer Eselsberg D-7900 ULM, Germany
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we investigate the zeros of power series

1

for some functions of coefficients A. In particular, we derive upper and lower bounds for the number of zeros of f in its domain of analyticity.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1981

References

1. Ford, W., Studies on divergent series and summability and the asymptotic developments of functions defined by MacLaurin series, Chelsea Publ. Comp., New York, (1960).Google Scholar
2. Gawronski, W., Asymptotic distribution of the zeros of power series, Serd. Bulg. math. publ. vol. 5, 13. 23 (1979).Google Scholar
3. Gawronski, W. and Peyerimhoff, A., On the zeros of power series with rational coefficients, Arch. Math., 29, 173. 186 (1977).Google Scholar
4. Gawronski, W., On the zeros of power series with rational coefficients II, Arch. Math., 31, 346. 355 (1978).Google Scholar
5. Gawronski, W., On the zeros of power series with rational coefficients HI, Arch. Math., 32, 368. 376 (1979).Google Scholar
6. Gawronski, W., A lower bound for the number of negative zeros of power series, Canad. Math. Bull., vol. 22 (1), 47. 52 (1979).Google Scholar
7. Jurkat, W. B. and Peyerimhoff, A., On power series with negative zeros, Tôhoku Math. J., vol. 24, no. 2, 207. 221 (1972).Google Scholar
8. Olver, F., Introduction to asymptotics and special functions, Academic Press, Inc., New York, London, (1974).Google Scholar
9. Peyerimhoff, A., On the zeros of power series, Mich. Math. J., vol. 13, 193. 214 (1966).Google Scholar
10. Pôlya, G. and Szegô, G., Aufgaben und Lehrsâtze aus der Analysis I, II, Springer-Verlag, Berlin, Heidelberg, New York, (1970).Google Scholar
11. Sansone, G. and Gerretsen, J., Lectures on the theory of functions of a complex variable, vol. I, P. Noordhoff, Groningen, (1960).Google Scholar
12. Stadtmuller, U., On the zeros of power series with logarithmic coefficients, Canad. Math. Bull., vol. 22 (2), 221. 233 (1979).Google Scholar