On the evaluation of an integral connected with the thermonuclear reaction rate in closed form

The standard expression of the reaction rate for low‐energy, nonresonant nuclear reactions in nondegenerate plasma contains a parameter‐dependent integral which in all previous calculations with physical or astrophysical background is considered as not capable of being evaluated in a closed form. So one usually resorts to approximation methods concerning large values of the parameter. At first we point out that C ONSUL (1964) has given a series representation of the integral which was identified with a M EIJER 's G ‐function by M ATHAI (1971). Next, in view of a physically more exact determination of the reaction rate formula, especially in connection with calculations concerning stellar energy generation, we consider a more general integral containing the mentioned one as special case and give an approximation‐free representation by means of M EIJER 's G ‐function. The G ‐function so obtained may be conceived as complex‐valued continuation of C ONSUL 's series representation of a certain class of integrals contained in the considered one. From the series we extract a small parameter approximation of the special integral.