The complete form of moment equations of stellar dynamics

The exact mathematical expression for an arbitrary n-order stellar hydrodynamic equation is explicitly obtained depending on the central moments of the velocity distribution. In such a form the equations are physically meaningful, since they can be compared with the ordinary hydrodynamic equations of compressible, viscous fluids. The equations are deduced without any particular assumptions about symmetries, steadiness, or particular kinematic behaviours, so that they can be used in their complete form, and for any order, in future works with improved observational data. Also, in order to work with a finite number of equations and unknowns, which would provide a dynamic model for the stellar system, the n-order equation is needed to investigate in a more general way the closure conditions, which may be expressed in terms of velocity distribution statistics, as it is shown in a case example.