International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 2, Pages 115-119
doi:10.1155/S0161171202003393
Pythagorean identity for polyharmonic polynomials
1603F Simpson Street, Greensboro 27401, NC, USA
2Department of Mathematics, Syracuse University, Syracuse 13244, NY, USA
Received 13 May 1999
Copyright © 2002 Allan Fryant and Murali Krishna Vemuri. 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
Polyharmonic polynomials in n variables are shown to satisfy a
Pythagorean identity on the unit hypersphere. Application is made
to establish the convergence of series of polyharmonic
polynomials.