  An overview is presented on statistical techniques for the analytic
evaluation of integrals for non-resonant, non-resonant depleted, non-resonant
cut-off, non-resonant sccreened, and resonant thermonuclear reaction rates. The
techniques are based on statistical distribution theory and the theory of
Meijer's G-function and Fox's H-function. The implementation of Meijer's
G-function in Mathematica constituts an additional utility for analytic
manipulations and numerical computation of thermonuclear reaction rate
integrals. Recent results in the astrophysical literature related to the use of
analytic thermonuclear reaction rates are incorporated.
