International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 2, Pages 115-119

Pythagorean identity for polyharmonic polynomials

Allan Fryant1 and Murali Krishna Vemuri2

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.


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.