Peters polynomials

In mathematics, the Peters polynomials \( s_n(x) \) are polynomials studied by Peters (1956, 1956b) given by the generating function

\( \displaystyle \sum s_n(x)t^n/n! = \frac{(1+t)^x}{(1+(1+t)^\lambda)^{-\mu}} \)

(Roman 1984, 4.4.6), (Boas & Buck 1958, p.37). They are a generalization of the Boole polynomials.
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. 19, Berlin, New York: Springer-Verlag, MR 0094466
Peters, George Owen (1956), Schafer, Richard D., ed., "Boole polynomials of higher and negative orders", Bulletin of the A. M. S. 62 (1): 7, doi:10.1090/S0002-9904-1956-09972-0
Peters, George Owen (1956b), Schafer, Richard D., ed., "Boole polynomials and numbers of the second kind", Bulletin of the A. M. S. 62: 387, doi:10.1090/S0002-9904-1956-10046-3
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

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