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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Asymptotic factorial powers expansions for binomial and negative binomial reciprocals
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by Grzegorz A. Rempała PDF
Proc. Amer. Math. Soc. 132 (2004), 261-272 Request permission


By considering the variance formula for a shifted reciprocal of a binomial proportion, the asymptotic expansions of any order for first negative moments of binomial and negative binomial distributions truncated at zero are obtained. The expansions are given in terms of the factorial powers of the number of trials $n$. The obtained formulae are more accurate than those of Marciniak and Wesołowski (1999) and simpler, as they do not involve the Eulerian polynomials.
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Additional Information
  • Grzegorz A. Rempała
  • Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
  • Email:
  • Received by editor(s): March 1, 2001
  • Received by editor(s) in revised form: August 1, 2002
  • Published electronically: August 13, 2003

  • Dedicated: To my parents
  • Communicated by: Richard A. Davis
  • © Copyright 2003 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 132 (2004), 261-272
  • MSC (2000): Primary 60E05, 62E20; Secondary 11B15, 05A16
  • DOI:
  • MathSciNet review: 2021270