Peters polynomials

In mathematics, the Peters polynomials s_n(x) are polynomials studied by George Peters^{[1] [2]} given by the generating function

${\displaystyle \displaystyle \sum _{n=0}^{+\infty }s_{n}(x){\frac {t^{n}}{n!}}={\frac {(1+t)^{x}}{(1+(1+t)^{\lambda })^{\mu }}}}${\displaystyle \displaystyle \sum _{n=0}^{+\infty }s_{n}(x){\frac {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.

• Umbral calculus

• 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 978-0-387-03123-1, MR 0094466 {{citation}}: ISBN / Date incompatibility (help)
• 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