Vol. 26, No. 2, 1968

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ISSN: 0030-8730
Fractional integration and inversion formulae associated with the generalized Whittaker transform

H. M. (Hari Mohan) Srivastava

Vol. 26 (1968), No. 2, 375–377
Abstract

In the present note, we invoke the theories of the Mellin transform as well as fractional integration to investigate a solution of the integral equation

∫ ∞
(xt)σ−(1∕2)e−(1∕2)xtWk+ (1∕2),m(xt)f(t)dt = W (σ){f : x},x > 0,
0                                       k,m
(*)

which defines a generalized Whittaker transform of the unknown function f L2(0,) to be determined in terms of its image Wk,m(σ){f : x}.

It is shown that under certain constraints (*) can be reduced to the form of a Laplace integral which is readily solvable by familiar techniques.

Mathematical Subject Classification
Primary: 44.50
Milestones
Received: 27 November 1967
Published: 1 August 1968
Authors
H. M. (Hari Mohan) Srivastava