  Here an extended form of the reaction rate probability integral, in the case
of nonresonant thermonuclear reactions with the depleted tail and the right
tail cut off, is considered. The reaction rate integral then can be looked upon
as the inverse of the convolution of the Mellin transforms of Tsallis type
statistics of nonextensive statistical mechanics and stretched exponential as
well as that of superstatistics and stretched exponentials. The differential
equations satisfied by the extended probability integrals are derived. The idea
used is a novel one of evaluating the extended integrals in terms of some
special functions and then by invoking the differential equations satisfied by
these special functions. Some special cases of limiting situations are also
discussed.
