We consider the problem of parameter estimation for an ergodic diffusion with
Fisher-Snedecor invariant distribution, to be called Fisher-Snedecor diffusion.
We compute the spectral representation of its transition density, which
involves a finite number of discrete eigenfunctions (Fisher-Snedecor
polynomials) as well as a continuous part. We propose moments based estimators
(related to the Fisher-Snedecor polynomials) and prove their consistency and
asymptotic normality.