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A Class of Integral Transforms†

Published online by Cambridge University Press:  20 January 2009

Jet Wimp
Jet Wimp
Affiliation:
Midwest Research Institute, Kansas City, Missouri
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In this paper we discuss a new class of integral transforms and their inversion formula. The kernel in the transform is a G-function (for a treatment of this function, see ((1), 5.3) and integration is performed with respect to the argument of that function. In the inversion formula, the kernel is likewise a G-function, but there integration is performed with respect to a parameter. Known special cases of our results are the Kontorovitch-Lebedev transform pair ((2), v. 2; (3))

and the generalised Mehler transform pair (7)

These transforms are used in solving certain boundary value problems of the wave or heat conduction equation involving wedge or conically-shaped boundaries, and are extensively tabulated in (6).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 14 , Issue 1 , June 1964 , pp. 33 - 40
Copyright
Copyright © Edinburgh Mathematical Society 1964

References

REFERENCE

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