Asymptotic Eulerian expansions for binomial and negative binomial reciprocals

Marciniak, Ewa; Wesołowski, Jacek

doi:10.1090/S0002-9939-99-05105-9

Asymptotic Eulerian expansions for binomial and negative binomial reciprocals
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by Ewa Marciniak and Jacek Wesołowski

Proc. Amer. Math. Soc. 127 (1999), 3329-3338

DOI: https://doi.org/10.1090/S0002-9939-99-05105-9

Published electronically: May 3, 1999

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Abstract:

Asymptotic expansions of any order for expectations of inverses of random variables with positive binomial and negative binomial distributions are obtained in terms of the Eulerian polynomials. The paper extends and improves upon an expansion due to David and Johnson (1956-7).

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