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The Inverse Laplace Transform of the Product of Two Whittaker Functions

Published online by Cambridge University Press:  24 October 2008

F. M. Ragab
F. M. Ragab
Affiliation:
Cairo UniversityCairo
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Extract

The object of this paper is to obtain the original function of which the Laplace transform (l) is the product

where, as usual, p is complex, n is any positive integer, and Wk, m(z) is the Whittaker function defined by the equation

In § 2 it will be shown that this original function is

where the symbol Δ(n; α) represents the set of parameters

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 4 , October 1962 , pp. 580 - 582
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Erdélyi, A., et al. Tables of integral transforms, vol. 1 (McGraw-Hill; New York, 1954).Google Scholar
(2)Macrobert, T. M., Functions of a complex variable, 4th ed. (Macmillan; London, 1954).Google Scholar
(3)Macrobert, T. M., Multiplication formulae for the E-functions regarded as functions of their parameters. Pacific J. Math. 9 (1959), 759–761.CrossRefGoogle Scholar
(4) Bailey, W. N., Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (1927), 242–254.Google Scholar