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Let´s assume I have a function $f(\theta)>0$ defined for $\theta<\pi$ and $\theta >0$. I want to find its Legendre polynomial decomposition $f(\theta)= \sum_{l=0}^\infty f_l \, P_l(\cos{(\theta)})$. What is the condition that the coefficients $f_l$ must satisfy in order for $f(\theta)$ to be greater than zero?

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