Analytic forms of thermonuclear functions

In nuclear fusion reactions taking place in stellar interiors, if there is a deviation from hydrostatic equilibrium, then one can think of an alternative velocity distribution instead of the Maxwell–Boltzmann distribution. The paper is devoted to study the extension of non-resonant reaction rate integrals in standard, cut-off, depleted, and screened cases via Mittag-Leffler distribution. The extended non-resonant reaction rate integrals are represented in the form of Fox’s H-function, generalized Wright function. A comparison of the Mittag-Leffler non-resonant energy distributions with the standard Maxwell–Boltzmann energy distribution and the pathway energy distribution is also done.