International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 2, Pages 115-119
doi:10.1155/S0161171202003393

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

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.