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Asymptotic Eulerian expansions for binomial and negative binomial reciprocals
Author(s):
Ewa
Marciniak;
Jacek
Wesolowski
Journal:
Proc. Amer. Math. Soc.
127
(1999),
3329-3338.
MSC (1991):
Primary 60E05, 62E20;
Secondary 11B68, 05A16
Posted:
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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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:
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
Posted:
May 3, 1999
Communicated by:
Wei-Yin Loh
Copyright of article:
Copyright
1999,
American Mathematical Society
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