Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học được đăng trên tạp chí toán học quốc tế đề tài: Some certain properties of the generalized hypercubical functions | Letic et al. Advances in Difference Equations 2011 2011 60 http content 2011 1 60 o Advances in Difference Equations a SpringerOpen Journal RESEARCH Open Access Some certain properties of the generalized hypercubical functions 12 3 1 1 Dusko Letic Nenad Cakic Branko Davidovic Ivana Berkovic and Eleonora Desnica Correspondence iwtbg@beotel. net Technical High School Kragujevac Serbia Full list of author information is available at the end of the article Springer Abstract In this article the results of theoretical research of the generalized hypercube function by generalizing two known functions referring to the cube hypervolume and hypersurface and the recurrent relation between them have been presented. By introducing two degrees of freedom k and n and the third half-edge r we are able to develop the derivative functions for all three arguments and discuss the possibilities of their use. The symbolic evaluation numerical experiment and graphic presentation of the functions are realized using Mathcad Professional and Mathematica. MSC 2010 33E30 33E50 33E99 52B11. Keywords special functions hypercube function derivate 1. Introduction The hypercube function HC is a hypothetical function connected with multidimensional space. It belongs to the group of special functions so its testing is being performed on the basis of known functions of the type r-gamma -psi Zn-logarithm exp-exponential function and so on. By introducing two degrees of freedom k and n we generalize it from discrete to continual 1 2 . In addition we can advance from the field of the natural integers of the dimensions-degrees of freedom of cube geometry to the field of real and non-integer values where all the conditions concur for a more condense mathematical analysis of the function HC k n r . In this article the analysis is focused on the infinitesimal calculus application of the HC which is given in the generalized form. For research papers on the development of
