Humbert polynomials

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

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

Boas & Buck (1958, p.58).

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, ISBN 978-0-387-03123-1, MR 0094466
• Humbert, Pierre (1921), "Some extensions of Pincherle's Polynomials", Proceedings of the Edinburgh Mathematical Society, 39: 21–24, doi:10.1017/S0013091500035756