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