  The Maxwell-Boltzmannian approach to nuclear reaction rate theory is extended
to cover Tsallis statistics (Tsallis, 1988) and more general cases of
distribution functions. An analytical study of respective thermonuclear
functions is being conducted with the help of statistical techniques. The
pathway model, recently introduced by Mathai (2005), is utilized for
thermonuclear functions and closed-form representations are obtained in terms
of H-functions and G-functions. Maxwell-Boltzmannian thermonuclear functions
become particular cases of the extended thermonuclear functions. A brief review
on the development of the theory of analytic representations of nuclear
reaction rates is given.
