On the generalized Schuster density law

A special case of the generalized Schuster density law for stellar systems with spherical symmetry is discussed; here the exponent in the denominator is equal to i/2 where i is a positive integer. Special attention is paid to the situation 2 ≤ i ≤ 5 since then the mass distributions in almost all approximately spherical stellar systems and subsystems known to exist - e. g. dark coronae of galaxies, bulges and halos of spiral galaxies, as well as the systems with the classical Schuster density law - are included. With certain improvements one can also obtain more ample variants including the density continuously attaining zero at a finite radius, somewhat different descriptions of the mass distribution, as well as generalizations towards axial symmetry. It is shown among others, that a spheroid with this mass distribution (i=4) yields the same total mass as the exponential disc and that the mass distribution proposed by King belongs asymptotically to the generalized Schuster density law (i=3)