Proceedings of the Edinburgh Mathematical Society (Series 2)

Research Article

A Class of Integral Transforms

Jet Wimpa1

a1 Midwest Research Institute, Kansas City, Missouri

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))

S0013091500011202_eqn1

S0013091500011202_eqn2

and the generalised Mehler transform pair (7)

S0013091500011202_eqn3

S0013091500011202_eqn4

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).

(Received August 30 1963)

Footnotes

† This paper covers research supported by the Aeronautical Research Laboratories, Office of Aerospace Research, U.S.A.F. The author is indebted to Yudell Luke and Professor Arthur Erdélyi for their comments.