Hostname: page-component-78c5997874-4rdpn Total loading time: 0 Render date: 2024-11-20T00:30:08.200Z Has data issue: false hasContentIssue false
  • English
  • Français

Definite integrals involving Whittaker functions

Published online by Cambridge University Press:  24 October 2008

F. M. Ragab  and
M. A. Simary
F. M. Ragab
Affiliation:
Cairo University and Cairo High Institute of Technology
M. A. Simary
Affiliation:
Cairo University and Cairo High Institute of Technology
Get access Rights & Permissions [Opens in a new window]

Extract

Little is known about definite integrals for the Whittaker functions. The object of this paper is to establish such results and the following formulae are established

where the symbol means that in the expression following it i is to be replaced by –i and the two expressions are to be added.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 4 , October 1968 , pp. 1033 - 1039
Copyright
Copyright © Cambridge Philosophical Society 1968

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)MacRobert, T. M.Functions of a complex variable, 5 edit. (1962).Google Scholar
(2)MacRobert, T. M.Philos. Mag. 31, (1941).CrossRefGoogle Scholar
(3)Erdely, A., Magnus, W., Oberhettinger, F. and Tricomi, F.Higher transcendental functions, vol. I (McGraw Hill; New York, 1953).Google Scholar
(4)Ragab, F. M.Integrals involving Whittaker functions. Ann. Mat. Pura Appl. (4) 65 (1964) 49–80.CrossRefGoogle Scholar
(5)Ragab, F. M.Some formulae for the product of two Whittaker functions. Nederl. Akad. Wetensch. Indag. Math. 58, (1958), 430–434.CrossRefGoogle Scholar
(6)Ragab, F. M.(a) New integral representations of the modified Bessel functions of the second kind. (b) Multiple integrals involving product of the modified Bessel functions of the second kind. (c) E-transforms I. (d) E-transforms II. Mathematics Research Center (University of Wisconsin, 1965).Google Scholar
(7)Ragab, F. M. and Simary, M. A.Integrals involving products of generalized Whittaker functions. Proc. Cambridge Philos. Soc. 61 (1965), p. 429–432.CrossRefGoogle Scholar