In the theory of thermonuclear reaction rates, analytical evaluation of thermonuclear functions for non-resonant reactions, including cases with cut-off and depletion of the tail of the Maxwell–Boltzmann distribution function were considered in a series of papers by Mathai and Haubold [A.M. Mathai, H.J. Haubold, Modern Problems in Nuclear and Neutrino Astrophysics, Akademie-Verlag, Berlin, 1988]. In the present paper we study more general classes of thermonuclear functions by introducing a pathway parameter α, so that when α→1 the thermonuclear functions in the Maxwell–Boltzmannian case are recovered. We will also give interpretations for the pathway parameter α in the case of cut-off and in terms of moments. Non-extensive statistical mechanics, as developed by Tsallis [C. Tsallis, What should a statistical mechanics satisfy to reflect nature? Physica D 193 (2004) 3–34], provides the physical basis for the generalized thermonuclear functions considered in this paper.
