Consider $$F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$$$$|z|\le L$$$$0 \le \theta \le \pi$$By having knowledge of $F(\theta)$, how can one approximate $h(z)$? In addition, I know that $F$ is differentiable with respect to $\theta$.How can I model and solve such problem with unknown function $h(z)$ in Mathematica or any other programming language?There is an idea in which we write Fourier series for both $F$ and h then by solving or manipulation of the integral we approximate the coefficients.** $k$ is the wave number, don't confuse it with anything else.** $z$ might be a complex number, but in this case you can consider it as real.**Any idea on this problem would be extremely appreciated.
Approximate $h$ in $F(\theta)=\sin \theta \int_{-L}^{+L}h(z)e^{-ikz\cos \theta} \,dz$
matlab;quadrature;fourier analysis;mathematica