Actuarial polynomials

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

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

(Roman 1984), (Boas Buck).

• 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, ISBN 9783540031239, https://books.google.com/books?id=eihMuwkh4DsC 
• 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, https://books.google.com/books?id=JpHjkhFLfpgC  Reprinted by Dover, 2005
• Toscano, Letterio (1950), "Una classe di polinomi della matematica attuariale" (in Italian), Rivista di Matematica della Università di Parma 1: 459–470 

• Kim, Eun Woo; Jang, Yu Seon (2016). "Some Umbral Characteristics of the Actuarial Polynomials". Journal of the Chungcheong Mathematical Society 29 (1): 73–82. doi:10.14403/jcms.2016.29.1.73. http://koreascience.or.kr/journal/view.jsp?kj=CCSHBU&py=2016&vnc=v29n1&sp=73. 

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