On the nuclear energy generation rate in a simple analytic stellar model

For a shperically symmetric star in quasi-static equilibrium a simple analytic stellar model is presented. The common technique of integration theory of special functions for treating a special solution of the equations of stellar structure is described. As an example the sun can be considered as a fluid in hydrostatic equilibrium. The total net rate of nuclear energy generation, which is equal to the luminosity of the star, is evaluated analytically for a linear density distribution assumed for a simple stellar model. For several analytic representations of the nuclear energy generation rate the luminosity function is evaluated for the presented stellar model in closed form