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Qi, Feng; Niu, Da-Wei; Guo, Bai-Ni

Some identities for a sequence of unnamed polynomials connected with the Bell polynomials. (English) Zbl 1429.11056

Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 113, No. 2, 557-567 (2019).
Summary: In the paper, by virtue of (1) the Stirling inversion theorem and the binomial inversion theorem, (2) the Faà di Bruno formula and two identities for the Bell polynomials of the second kind, (3) a formula of higher order derivative for the ratio of two differentiable functions, the authors (1) present two explicit formulas, a determinantal expression, and a recursive relation for a sequence of unnamed polynomials, (2) derive two identities connecting the sequence of unnamed polynomials with the Bell polynomials, (3) recover a known identity connecting the sequence of unnamed polynomials with the Bell polynomials.

Cited in 20 Documents

MSC:

11B83 Special sequences and polynomials
05A15 Exact enumeration problems, generating functions
11B73 Bell and Stirling numbers

Keywords:

identity; Bell polynomial; unnamed polynomial; explicit formula; inversion theorem; Stirling number; binomial coefficient
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Full Text: DOI DOI

References:

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