Astrophysical Thermonuclear Functions for Boltzmann-Gibbs Statistics and   Tsallis Statistics
  We present an analytic proof of the integrals for astrophysical thermonuclear functions which are derived on the basis of Boltzmann-Gibbs statistical mechanics. Among the four different cases of astrophysical thermonuclear functions, those with a depleted high-energy tail and a cut-off at high energies find a natural interpretation in q-statistics. 
R.K. Saxena, A.M. Mathai, H.J. Haubold