Dispersion relation in a plasma with arbitrary degeneracy

In a slightly degenerate plasma (or classical plasma) electronic waves generated consistently by the collective motion of particles, obey the Bohm-Gross dispersion relation [1], and in an extreme degenerate plasma (or quantum plasma) they obey the Silin one [2]. The essential difference between these two cases is the value of the electronic temperature (for a given plasma density). Our aim is to find a single dispersion relation which regroups these two limits. The case of vanishing temperature is investigated for the whole range of frequencies.