Generalized Appell polynomials

In mathematics, a polynomial sequence ${\displaystyle \{p_{n}(z)\}}$ has a generalized Appell representation if the generating function for the polynomials takes on a certain form:

where the generating function or kernel ${\displaystyle K(z,w)}$ is composed of the series

and

and

Given the above, it is not hard to show that ${\displaystyle p_{n}(z)}$ is a polynomial of degree ${\displaystyle n}$.

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