Abstract and Applied Analysis
Volume 2010 (2010), Article ID 364292, 17 pages
doi:10.1155/2010/364292
Research Article

The Hyperspherical Functions of a Derivative

Nenad Cakic,1 Duško Letic,2 and Branko Davidovic3

1Faculty of Electrical Engineering, University of Belgrade, 11000 Belgrade, Serbia
2Technical Faculty M. Pupin, 23000 Zrenjanin, Serbia
3Technical High School, 34000 Kragujevac, Serbia

Received 18 March 2010; Revised 5 October 2010; Accepted 15 November 2010

Academic Editor: L. L. Littlejohn

Copyright © 2010 Nenad Cakic et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.