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The H-function transform

Published online by Cambridge University Press:  09 April 2009

K. C. Gupta  and
P. K. Mittal
K. C. Gupta
Affiliation:
Department of MathematicsMalaviya Regional Engineering CollegeJaipur (India)
P. K. Mittal
Affiliation:
Government CollegeAjmer (India)
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Here we introduce a new integral transform whose kernel is the H-function. Since most of the important functions occurring in Applied Mathematics and Physics are special cases of the H-function, various integral transforms involving these functions as kernels follow as special cases of our transform. We mention some of them here and observe that a study of this transform gives general and useful results which serve as key formulae for several important integral transforms viz. Laplace transform, Hankel transform. Stieltjes transform and the various generalizations of these transforms. In the end we establish an inversion formula for the new transform and point out its special cases which are generalizations of results found recently.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 2 , May 1970 , pp. 142 - 148
Copyright
Copyright © Australian Mathematical Society 1970

References

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