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).^[1]