Humbert polynomials

In mathematics, the Humbert polynomials πλn,m(x) are a generalization of Pincherle polynomials introduced by Pierre Humbert given by the generating function

$(1-mxt+t^m{)}^{-\lambda }=\sum _{n=0}^{\mathrm{\infty }}{\pi }_{n,m}^{\lambda }(x)t^n$

(Boas Buck).

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 (Berlin, New York: Springer-Verlag) 19, ISBN 978-0-387-03123-1, https://books.google.com/books?id=eihMuwkh4DsC