Humbert polynomials
From HandWiki
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
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
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