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An inversion formula for the Varma transform

Published online by Cambridge University Press:  24 October 2008

R. K. Saxena
R. K. Saxena
Affiliation:
Department of Mathematics, McGill University, Montreal, Canada
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Abstract

Recently Fox ((5)) has given an inversion formula for the transform whose kernel is xνKν(x), where Kν(x) is the modified Bessel function of the second kind, by the application of fractional integration theory. In the present paper it has been shown that the integral equation

can be thrown into the form of a Laplace integral, with the help of fractional integration, which can be solved by known methods.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 62 , Issue 3 , July 1966 , pp. 467 - 471
Copyright
Copyright © Cambridge Philosophical Society 1966

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References

REFERENCES

(1)Erdelyi, A.On some functional transformations. Univ. e Politec. Torino, Rend. Setn. Mat. 10 (1940), 217–234.Google Scholar
(2)Erdelyi, A.et al. Tables of integral transforms, vol. i. (McGraw-Hill; New York, 1954).Google Scholar
(3)Goldstein, S.Operational representation of Whittaker's confluent hypergeometric function and Weber's parabolic cylinder functions. Proa. London Math. Soc. 34 (1932), 103–125.CrossRefGoogle Scholar
(4)Fox, C.Integral transforms based upon fractional integration. Proc. Cambridge Philos. Soc. 50 (1963), 63–71.CrossRefGoogle Scholar
(5)Fox, C.An inversion formula for a kernel K ν(x). Proc. Cambridge Philos. Soc. 61 (1965), 457–467.CrossRefGoogle Scholar
(6)Kober, H.On fractional integrals and derivatives. Quart. J. Math. Oxford, Ser. 2, 11 (1940), 193–211.CrossRefGoogle Scholar
(7)Saxena, R. K.Some theorems on generalized Laplace transform. I. Proc. Nat. Inst. Sci. India, Part A, 26 (1960), 400–413.Google Scholar
(8)Saxena, R. K.Some theorems on generalized Laplace transform. II. Riv. Mat. Univ. Parma, 2 (1962), 287–300.Google Scholar
(9)Saxena, R. K.Certain properties of Varma transform involving Whittaker functions. Collet. Math. 16 (1964).Google Scholar
(10)Titchmarsh, E. C.An introduction to the theory of Fourier integrals (Oxford, 1937).Google Scholar
(11)Varma, R. S.On a generalization of Laplace integral. Proc. Nat. Acad. Sci. India, Sect. A, 20 (1951), 209–216.Google Scholar
(12)Weyl, H.Viertelj. Naturf. Ges. Zürich, 62 (1917), 296–302.Google Scholar
(13)Whittaker, E. T. and Watson, G. N.A course of modern analysis (Cambridge, 1962).Google Scholar