Asymptotic Eulerian expansions for binomial and negative binomial reciprocals. (English) Zbl 0930.60004

Summary: 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 F. N. David and N. L. Johnson [Metron 18, No. 1/2, 77-81 (1956; Zbl 0074.35601)].


60E05 Probability distributions: general theory
11B68 Bernoulli and Euler numbers and polynomials
05A16 Asymptotic enumeration
62E20 Asymptotic distribution theory in statistics


Zbl 0074.35601
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