International Journal of Mathematics and Mathematical Sciences 
Volume 6 (1983), Issue 1, Pages 145-160
doi:10.1155/S0161171283000137

The continuous Jacobi transform

E. Y. Deeba1 and E. L. Koh2

 1Department of Mathematical Sciences, University of Petroleum and Minerals, Dhahran, Saudi Arabia
2Department of Mathematics and Statistics, University of Regina, Regina S4S 4J5, Canada
Received 20 April 1982; Revised 15 October 1982

Abstract

The purpose of this paper is to define the continuous Jacobi transform as an extension of the discrete Jacobi transform. The basic properties including the inversion theorem for the continuous Jacobi transform are studied. We also derive an inversion formula for the transform which maps L1(R+) into Lw2(−1,1) where w(x)=(1−x)α(1+x)β.