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).

• 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 {{citation}}: ISBN / Date incompatibility (help)