Boas–Buck polynomials

In mathematics, Boas–Buck polynomials are sequences of polynomials ${\mathrm{\Phi }}_n^{(r)}(z)$ defined from analytic functions $B$ and $C$ by generating functions of the form

$C(z{t}^{r}B(t))=\sum _{n\ge 0}{\mathrm{\Phi }}_n^{(r)}(z)t^n$.

The case $r=1$, 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