The Fermi function that appears in the beta spectrum formula accounts for the Coulomb attraction / repulsion between the emitted beta and the final state nucleus. Approximating the associated wavefunctions to be spherically symmetric, the Fermi function can be analytically calculated to be:
where  is the final momentum, Γ the Gamma function, and (if  is the fine-structure constant and  the radius of the final state nucleus) ,  (+ for electrons, − for positrons), and .
For non-relativistic betas (), this expression can be approximated by:
Other approximations can be found in the literature.