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Asymptotic Eulerian expansions for binomial and negative binomial reciprocals |
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| Authors: | Ewa Marciniak Jacek Wesolowski |
| Institution: | Mathematical Institute, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland ; Mathematical Institute, Warsaw University of Technology, Plac Politechniki 1, 00-661 Warsaw, Poland |
| 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). |
| Keywords: | Eulerian numbers Eulerian polynomials asymptotic series expansions inverse moments positive binomial distribution positive negative binomial distribution |
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