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In mathematics, the actuarial polynomials a(β)
n(x) are polynomials studied by Toscano (1950) given by the generating function

\( \displaystyle \sum_n \frac{a_n^{(\beta)}(x)}{n!}t^n = \exp(\beta t +x(1-e^t)) \)

(Roman 1984, 4.3.4), Boas & Buck (1958).

See also

Umbral calculus


Boas, Ralph P.; Buck, R. Creighton (1958), Polynomial expansions of analytic functions, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge. 19, Berlin, New York: Springer-Verlag, MR 0094466
Roman, Steven (1984), The umbral calculus, Pure and Applied Mathematics 111, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], ISBN 978-0-12-594380-2, MR 741185 Reprinted by Dover, 2005
Toscano, Letterio (1950), "Una classe di polinomi della matematica attuariale", Rivista di Matematica della Università di Parma (in Italian) 1: 459–470, MR 0040480, Zbl 0040.03204

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