# Legendre polynomial expansion of a positive function

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?