Boas–Buck polynomials

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

${\displaystyle \displaystyle C(zt^{r}B(t))=\sum _{n\geq 0}\Phi _{n}^{(r)}(z)t^{n}}$.

The case ${\displaystyle r=1}$, 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., vol. 19, Berlin, New York: Springer-Verlag, ISBN 9783540031239, MR 0094466