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International Journal of Mathematics and Mathematical Sciences
Volume 8, Issue 2, Pages 345-354

The second continuous Jacobi transform

1Department of Applied Mathematical Sciences, University of Houston–Downtown, Houston, Texas 77002, USA
2Department of Mathematics and Statistics, University of Regina, Regina S4S 0A2, Canada

Received 14 February 1984

Copyright © 1985 Hindawi Publishing Corporation. 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.


This paper continues the work started in [1]; a second continuous Jacobi transform is defined for suitable functions f(x). Properties of the transform are studied. In particular, the first continuous Jacobi transform in [1] and the second continuous Jacobi transform are shown to be inverse to each other. The paper concludes with an extension of Campbell's sampling theorem [2].