Analytic expansions of thermonuclear reaction rates

The evaluation of thermonuclear reaction rates requires the calculation of several thermonuclear functions. These functions can be written as the Laplace transform of locally integrable functions which have an asymptotic expansion in negative rational powers of their variable. In this paper we obtain asymptotic expansions of the Laplace transform of these kinds of functions for small values of the parameter of the transformation. Error bounds are obtained at any order of the approximation for a large family of Laplace transforms which include thermonuclear functions. Then we apply this asymptotic theory to the calculation of convergent expansions of four thermonuclear functions in powers of the dimensionless Sommerfeld parameter. Some of these expansions also involve logarithmic terms in the dimensionless Sommerfeld parameter. Accurate error bounds are given at any order of the approximation