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Calculation of the indicator of an entire function of rational order in terms of its taylor coefficients

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Abstract

By using both the Pólya theorem on the connection between the growth of an entire exponential function and the location of singularities of its Borel transform and the analog of this result for finite-order entire functions (due to Mclntyre), we obtain estimates for the indicator of the growth of an entire function in terms of its Taylor coefficients and, in some cases, determine this indicator exactly.

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References

  1. M. M. Dzhrbashyan,Integral Transformations and Representations of Functions in a Complex Region [in Russian], Nauka, Moscow (1966).

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  2. A. Denjoy, “Sur les singularités d'une fonction analitique définie par un élément,”C. R. Acad. Sci.,206, 737 (1938).

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  3. B. Ya. Levin,Distribution of the Roots of Entire Functions [in Russian], Gostekhteoretizdat, Moscow (1956).

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Authors and Affiliations

  1. Moscow Pedagogical Institute, Moscow

    G. G. Braichev

Authors
  1. G. G. Braichev
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Additional information

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 6, pp. 854–858, June, 1993.

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Braichev, G.G. Calculation of the indicator of an entire function of rational order in terms of its taylor coefficients. Ukr Math J 45, 943–948 (1993). https://doi.org/10.1007/BF01061444

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  • DOI: https://doi.org/10.1007/BF01061444

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