  The method for the evaluation of the non-resonant thermonuclear function in
the Maxwell-Boltzmann case with depleted tail is discussed. Closed forms of the
analytical results are obtained in computational format, and written in terms
of the H-function in two variables. The standard non-resonant cases are
extended to Tsallis reaction rates through the pathway model. Behavior of the
depleted non-resonant thermonuclear function is studied. A comparison of the
Maxwell-Boltzmann energy distribution with a more general energy distribution
called pathway energy distribution is also done.
