Boas–Buck polynomials

In mathematics, Boas–Buck polynomials are sequences of polynomials [math]\displaystyle{ \Phi_n^{(r)}(z) }[/math] defined from analytic functions [math]\displaystyle{ B }[/math] and [math]\displaystyle{ C }[/math] by generating functions of the form

[math]\displaystyle{ \displaystyle C(zt^r B(t))=\sum_{n\ge0}\Phi_n^{(r)}(z)t^n }[/math].

The case [math]\displaystyle{ r=1 }[/math], sometimes called generalized Appell polynomials, was studied by Boas and Buck (1958).

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 9783540031239, https://books.google.com/books?id=eihMuwkh4DsC