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Given the sequences $a_n$, $b_n$ and $c_n=a_n b_n$. Let $F(x) =\sum a_n x^n$, $G(x) =\sum b_n x^n$, $H(x) =\sum c_n x^n$ be the formal power series of the given sequences.

Can you generally express $H(x)$ as function of $F(x)$ and $G(x)$? What would that look like?

MennoK
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    Apparently $H(z) = \frac{1}{2\pi} \int_0^{2\pi}F(\sqrt z e^{it}) G(\sqrt z e^{-it}) dt$, cf https://en.wikipedia.org/wiki/Generating_function_transformation#Hadamard_products_and_diagonal_generating_functions. Keyword is Hadamard product. But I doubt this will have a simple form in most cases. – Milten Aug 14 '21 at 15:58
  • @Milten I will look into it, thanks! – MennoK Aug 14 '21 at 15:59

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