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Apostol–Euler polynomials and asymptotics for negative binomial reciprocals
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In this parer, we investigate the inverse moments of a generalized negative binomial distribution nb(a,p), where a is an arbitrary positive real number. We prove asymptotic expansions of any order for the r-th inverse moments, r being also an arbitrary positive real number. These expansions are expressed in terms of the so-called Apostol-Euler polynomials.
Abstract
In this parer, we investigate the inverse moments of a generalized negative binomial distribution nb(a,p), where a is an arbitrary positive real number. We prove asymptotic expansions of any order for the r-th inverse moments, r being also an arbitrary positive real number. These expansions are expressed in terms of the so-called Apostol-Euler polynomials.
참고문헌 (7)
- L. Comtet, "Advanced combinatorics" (1974), Reidel
- Q-M. Luo, "Apostol–Euler polynomials of higher order and gaussian hypergeometric functions", Taiwanese Journal of Mathematics, 10, pp.917~925 (2006)
- E. Marciniak, "Asymptotic eulerian expansions for binomial and negative binomial reciprocals", Proc. Amer. Math. Soc, 127, pp.3329~3338 (1999)
- N.M. Temme, "Special functions: An introduction to the classical functions of mathematical physics" (1996), John Wiley and Sons, Inc.
- R. Wong, "Asymptotic Approximations of Integrals" (2001), SIAM Philadelphia
- Wuyungaoa, T. Wang, "Asymptotic expansions for inverse moments of binomial and negative binomial", Statistics and Probability Letters, 78, pp.3018~3022 (2008)
- M. Znidaric, "Asymptotic expansion for inverse moments of binomial and Poisson distributions", The Open Statistics & Probability Journal, pp.7~10 (2009)
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