A linear binomial recurrence and the Bell numbers and polynomials | Zendy

H. W. Gould | Zendy; Jocelyn Quaintance | Zendy

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A linear binomial recurrence and the Bell numbers and polynomials

Author(s) -

H. W. Gould,

Jocelyn Quaintance

Publication year - 2007

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm0702371g

Subject(s) - mathematics , bell polynomials , binomial coefficient , binomial (polynomial) , binomial theorem , discrete mathematics , pure mathematics , combinatorics , algebra over a field , statistics

Let B(n) denote the nth Bell number. It is well known that B(n) obeys the recurrence relation (0.1) . The goal of this paper is to study arbitrary functions f(n) that obey (0.1), namely (0.2) . By iterating (0.2), f(n + r) can be written as a linear combination of binomial coeffcients with polynomial coefficients . The polynomials have various interesting properties. This paper provides a sampling of these properties including two new ways to represent B(n) in terms of .

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