Journal of Applied Mathematics and Stochastic Analysis
Volume 8 (1995), Issue 1, Pages 85-90

New generating functions for multivariate biorthogonal polynomials on the N-sphere

Harold Exton

“Nyuggel”, Lunabister, Dunrossness, Shetland, ZE2 9JH, United Kingdom

Received 1 July 1994; Revised 1 December 1994

Copyright © 1995 Harold Exton. 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.


Certain multivariate biorthogonal polynomials on the N-sphere arise in connection with quantum chromodynamics. These functions can be expressed in terms of Lauricella functions of the first kind, and multi-dimensional generating functions for them are deduced by means of an extension of Bailey's theorem.