Actuarial polynomials

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

∑ n a n ( β ) ( x ) n ! t n = exp ⁡ ( β t + x ( 1 − e t ) ) {\displaystyle \displaystyle \sum _{n}{\frac {a_{n}^{(\beta )}(x)}{n!}}t^{n}=\exp(\beta t+x(1-e^{t}))}

[1][2][3]

See also

  • Umbral calculus

References

  • Boas, Ralph P.; Buck, R. Creighton (1958), Polynomial expansions of analytic functions, Ergebnisse der Mathematik und ihrer Grenzgebiete. Neue Folge., vol. 19, Berlin, New York: Springer-Verlag, ISBN 9783540031239, MR 0094466
  • Roman, Steven (1984), The umbral calculus, Pure and Applied Mathematics, vol. 111, London: Academic Press Inc. [Harcourt Brace Jovanovich Publishers], ISBN 978-0-12-594380-2, MR 0741185 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

Further reading

  • 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.


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  1. ^ Toscano (1950).
  2. ^ Roman (1984), 4.3.4.
  3. ^ Boas & Buck (1958).