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I have a sequence of polynomials defined in the following way:

[tex]P_k(x) = \frac{\partial^k}{\partial x^k}e^{s(x)}\vert_{x=0}[/tex]

Essentially the polynomial P_{k}is thek-th derivative of [itex]\exp(s(x))[/itex] evaluated at x=0. The function s(x) is a polynomial of 2nd degree in x.

In mathematica I define the polynomials with the following code:

D[Exp[s[x]], {x, k}]

For k=1..n one obtains a list of n polynomials P_{1}(x),...,P_{n}(x).

My question is: is it possible to ask Mathematica to find a recurrent relation that expresses any P_{k}as a function of the previous polynomials P_{k-1}, P_{k-2}... ? (assuming it exists).

A similar well-known problem exists for http://en.wikipedia.org/wiki/Hermite_polynomials#Definition"

Thanks.

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# Finding recursive relations in Mathematica

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