On power series, Bell polynomials, Hardy-Ramanujan-Rademacher problem and its statistical applications. (English) Zbl 0826.30002

Voinov, Vasily; Nikulin, Mikhail

Kybernetika 30, No. 3, 343-358 (1994).

A formula is derived for finding the common term of a power series which is an arbitrary complex power of a polynomial. This formula provides expressions for direct evaluation of the number of partitions of a nonnegative integer and the partitions themselves, which are useful in evaluating probabilities of distributions of order \(k\), derivatives of composite functions, and Bernoulli, Euler and Bell polynomials. Alternative expressions for the truncated Bell polynomials and some statistical applications are also given.

Reviewer: A.N.Philippou (Nicosia)

MSC:

30B10	Power series (including lacunary series) in one complex variable
05A17	Combinatorial aspects of partitions of integers
11B68	Bernoulli and Euler numbers and polynomials
62G05	Nonparametric estimation

Keywords:

Euler polynomials; Bernoulli polynomials; Bell polynomials

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