  Possible modification in the velocity distribution in the non-resonant
reaction rates leads to an extended reaction rate probability integral. The
closed form representation for these thermonuclear functions are used to obtain
the stellar luminosity and neutrino emission rates. The composite parameter {C}
that determines the standard nuclear reaction rate through the
Maxwell-Boltzmann energy distribution is extended to {C}^* by the extended
reaction rates through a more general distribution than the Maxwell-Boltzmann
distribution. The new distribution is obtained by the pathway model introduced
by Mathai in 2005 [Linear Algebra and Its Applications, 396, 317-328]. Simple
analytic models considered by various authors are utilized for evaluating
stellar luminosity and neutrino emission rates and are obtained in generalized
special functions such as Meijer's G-function and Fox's H-function. The
standard and extended non-resonant thermonuclear functions are compared by
plotting them. Behavior of the new energy distribution, more general than
Maxwell-Boltzmann is also studied.
