Present status of the theory and analytic evaluation of non-resonant thermonuclear reaction rates

Concerning the analytic evaluation of reaction rates it is proposed to use the integration theory of special functions. For the special case of thermonuclear reactions in non-degenerate, nonrelativistic plasma it is shown that the non-resonant reaction rate can be evaluated in closed form by means of generalized hypergeometric functions. In connection with these closed-form results one can give differential and functional relations and series expansions. Also approximation considerations can be performed. (author)