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So, I have to approximate $f(x) = cos(x)$ using a second-degree polynomial.

$ P(x)=\sum_{i=0}^2 c_i \pi_i(x) $

$\pi_i$ is the Laguerre polynomial. My professor instructed me that I can use the following formula to calculate $c_i$:

$ c_i=(\pi_i,f)/(\pi_i,\pi_i) $

But I'm having a hard time making sense of that. Isn't $c_i$ a scalar? By that formula, I seem to get a vector with two components.

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Here $(g,h)$ should denote the scalar product defined by $(g,h)=\int_0^{\infty}g(t)h(t)e^{-t}dt$