where Ne is the electron density, NZ the number density of hydrogenic (bare) ions of nuclear charge Z, IH the ionization energy of hydrogen, n′ the principal quantum number of the lowest level for which adjacent levels are so close that they approach a continuum and summation over n may be replaced by an integral. (The choice of n′ is rather arbitrary; n′ as low as 6 is found in the literature.) γf b and γf f are the Gaunt factors, which are generally close to unity. (For the higher free-bound continua, starting with n′ + 1, an average Gaunt factor f b is used.) For neutral hydrogen, the recombination continuum forming H- becomes important, too .
In the equation above, the value of the constant factor is
Near the ionization limit, the f values for bound-bound transitions of a spectral series (n′ → ∞) make a smooth connection to the differential oscillator strength distribution df/dε in the continuum .