Generalized Appell polynomials

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

Related Topics:
Mathematics - Polynomial sequence - Generating function - Polynomial

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:K(z,w) = A(w)Psi(zg(w)) = sum_{n=0}^infty p_n(z) w^n

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where the generating function or kernel K(z,w) is composed of the series

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:A(w)= sum_{n=0}^infty a_n w^n quad with a_0 e 0

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and

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:Psi(t)= sum_{n=0}^infty Psi_n t^n quad and all Psi_n e 0

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and

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:g(w)= sum_{n=1}^infty g_n w^n quad with g_1 e 0.

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Given the above, it is not hard to show that p_n(z) is a polynomial of degree n.

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