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

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.

### 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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### References:

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