Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-24T01:22:47.977Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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