Humbert polynomials

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

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

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, MR 0094466
• Humbert, Pierre (1921), "Some extensions of Pincherle's Polynomials", Proceedings of the Edinburgh mathematics society, 39: 21–24, doi:10.1017/S0013091500035756