Boas–Buck polynomials

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

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

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., 19, Berlin, New York: Springer-Verlag, ISBN 9783540031239, https://books.google.com/books?id=eihMuwkh4DsC 

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