Abstract

In the present paper an attempt has been made to show that Ifunction and a finite sum of H-functions form a pair of unsymmetrical Fourier kernels under a specified set of conditions. The reciprocity has been established by the method of mean square convergence. In addition, a set of sufficient conditions for uniform convergence of the I-function has also been obtained as a concomitant result. Further, result obtained by Kesarwani [6,7] for unsymmetrical Fourier kernels follow as special cases.

Keywords and Phrases

Unsymmetrical Fourier kernels, H-function, I-function, Mellin transform.

A.M.S. subject classification

33E20.

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