Journal of Applied Mathematics
Volume 2003 (2003), Issue 11, Pages 569-573

On a zonal polynomial integral

A. K. Gupta1 and D. G. Kabe2

1Department of Mathematics and Statistics, Bowling Green State University, Bowling Green 43403-0221, OH, USA
2Department of Mathematics and Computer Science, Saint Mary's University, Halefax B3H 3C3, Nova Scotia, Canada

Received 2 September 2002; Revised 9 July 2003

Copyright © 2003 A. K. Gupta and D. G. Kabe. 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.


A certain multiple integral occurring in the studies of Beherens-Fisher multivariate problem has been evaluated by Mathai et al. (1995) in terms of invariant polynomials. However, this paper explicitly evaluates the context integral in terms of zonal polynomials, thus establishing a relationship between zonal polynomial integrals and invariant polynomial integrals.