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Natalini, Pierpaolo; Ricci, Paolo Emilio

Higher order Bell polynomials and the relevant integer sequences. (English) Zbl 1499.05021

Appl. Anal. Discrete Math. 11, No. 2, 327-339 (2017).
Summary: The recurrence relation for the coefficients of higher order Bell polynomials, i.e. of the Bell polynomials relevant to \(n\)th derivative of a multiple composite function, is proved. Therefore, starting from this recurrence relation and by using the computer algebra program Mathematica, some tables for complete higher order Bell polynomials and the relevant numbers are derived.

Cited in 10 Documents

MSC:

05A10 Factorials, binomial coefficients, combinatorial functions
11P81 Elementary theory of partitions
26A06 One-variable calculus

Keywords:

combinatorial analysis; differentiation of composite functions; higher-order Bell polynomials and number; Bell polynomials; partitions

Software:

OEIS; Mathematica
Cite Review PDF
Full Text: DOI

Online Encyclopedia of Integer Sequences:

Square array A(n,k), n >= 0, k >= 0, read by antidiagonals, where the e.g.f. of column k is 1+g^(k+1)(x) with g = x-> exp(x)-1.

References:

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[26] Pierpaolo Natalini (Received 19.07.2016.)
[27] Dipartimento di Matematica e Fisica -(Revised 20.03.2017.)
[28] Università degli Studi Roma Tre Largo San Leonardo Murialdo, 1 -00146 -Roma (Italia) E-mail: natalini@mat.uniroma3
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