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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Asymptotic Eulerian expansions
for binomial and negative binomial reciprocals


Authors: Ewa Marciniak and Jacek Wesolowski
Journal: Proc. Amer. Math. Soc. 127 (1999), 3329-3338
MSC (1991): Primary 60E05, 62E20; Secondary 11B68, 05A16
Published electronically: May 3, 1999
MathSciNet review: 1637400
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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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Additional Information

Ewa Marciniak
Affiliation: Mathematical Institute, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland
Email: wesolo@alpha.im.pw.edu.pl

Jacek Wesolowski
Affiliation: Mathematical Institute, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05105-9
PII: S 0002-9939(99)05105-9
Keywords: Eulerian numbers, Eulerian polynomials, asymptotic series expansions, inverse moments, positive binomial distribution, positive negative binomial distribution
Received by editor(s): January 14, 1998
Published electronically: May 3, 1999
Communicated by: Wei-Yin Loh
Article copyright: © Copyright 1999 American Mathematical Society