[en] By use of a highly efficient theory of generalized hypergeometric functions, we show that the non-resonant thermonuclear reaction rate can be evaluated in closed form. This new approach is advantageous to operate analytically with reaction rates. The numerical computation of the rate may be performed with the aid of associated differential equation, a convergent series expansion for small values of the characteristic parameter and an asymptotic expansion of large values of the characteristic parameter. (orig.)