Humbert polynomials

In mathematics, the Humbert polynomials πλn,m(x) are a generalization of Pincherle polynomials introduced by Humbert (1921) given by the generating function

[math]\displaystyle{ \displaystyle (1-mxt+t^m)^{-\lambda}=\sum^\infty _{n=0}\pi^\lambda_{n,m}(x)t^n }[/math]

(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, https://books.google.com/books?id=eihMuwkh4DsC 
• Humbert, Pierre (1921), "Some extensions of Pincherle's Polynomials", Proceedings of the Edinburgh Mathematical Society 39: 21–24, doi:10.1017/S0013091500035756