The Hyperspherical Functions of a Derivative

Abstract

We present the results of theoretical research of the generalized hypersherical function (HS) by generalizing two known functions related to the sphere hypersurface and hypervolume and the recurrent relation between them. By introducing two-dimensional degrees of freedom $k$ and $n$ (and the third, radius $r$), we develop the derivative functions for all three arguments and the possibilities of their use. The symbolical evolution, numerical experiment, and graphical presentation of functions are realized using the Mathcad Professional and Mathematica softwares.