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A generating function is a way of encoding an infinite sequence of numbers by treating them as the coefficients of a formal power series. Tag questions involving generating functions in this.

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functional equation, how to solve

Suppose $x_i, y_i \in \mathbb{R}^n$, and $F,G: \mathbb{R}^n \times \mathbb{R}^n \to \mathbb{R}^n$. $$F(x, y) = \frac{x\circ Ay}{x^TAy}$$ $$G(x, y) = \frac{x\circ By}{x^TBy}$$ where $A$ and $B$ are som …