Advertisement

On a simultaneous characterization of the poisson law and the gamma distribution

  • R R Hall
  • I Vincze
Conference paper
Part of the Lecture Notes in Mathematics book series (LNM, volume 861)

Abstract

The authors consider the following problem due to A Rényi and I Vincze: if for the entire function f(t)=1+a1t+a2t2+. ... with positive coefficients we have Open image in new window then is it necessary that f(t) ≡ et? Some results in this direction were proved in [2], [5]. Now it is shown that if 1/f is completely monotone then we must have f(t) ≡ et.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Freud, G., Restglied eines Teuberschen Satzes I, Acta Math. Acad. Sci. Hungar., 2 (1951) 299–308.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    Hall, R.R. and Williamson, J.H., On a certain functional equation, J. London Math. Soc., 12 (1976), 133–136.MathSciNetCrossRefzbMATHGoogle Scholar
  3. [3]
    Hausdorff, F., Summationsmethoden und momenten folgen I, Math. Zeitschrift, 9 (1921) 74–109.MathSciNetCrossRefGoogle Scholar
  4. [4]
    Hayman, W.K., Research problems in function theory, Athlone, London, 1967.zbMATHGoogle Scholar
  5. [5]
    Hayman, W.K. and Vincze, I., A problem on entire functions, Complex Analysis and its Applications, dedicated to I.N. Vekua on his 70th birthday. Izd. Nauka, Moskow 1978, 191–194.Google Scholar
  6. [6]
    Rényi, A., On a new axiomatic theory of probability, Acta Math. Acad. Sci. Hungar., 6 (1965) 185–335.MathSciNetGoogle Scholar
  7. [7]
    Sarkodi, K., A rule of dualism in mathematical Statistics, Acta Math. Acad. Sci. Hungar., 9 (1960) 83–92.MathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • R R Hall
    • 1
    • 2
  • I Vincze
    • 1
    • 2
  1. 1.Department of MathematicsUniversity of YorkYorkEngland
  2. 2.Department of Mathematical StatisticsMathematical Institute of the Hungarian Academy of SciencesBudapest

Personalised recommendations