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Integrals involving E-functions

Published online by Cambridge University Press:  18 May 2009

F. M. Ragab  and
M. A. Simary
F. M. Ragab
Affiliation:
Cairo University, Cairo, Egypt
M. A. Simary
Affiliation:
Cairo High Institute of Technology, Helwan, Egypt
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In this paper two integrals involving E-functions are evaluated in terms of E-functions. The formulae to be established are:

where n is a positive integer,

and

where n is a positive integer,

and

the prime and the asterisk denoting that the factor sin {(s–s)π/2n} and the parameter βq+s–βq+s + 1 are omitted. The definitions and properties of MacRobert's E-function can be found in [1, pp. 348–352] and [3, pp. 203–206].

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 7 , Issue 4 , July 1966 , pp. 174 - 177
Copyright
Copyright © Glasgow Mathematical Journal Trust 1966

References

REFERENCES

1.MacRobert, T. M., Functions of a Complex Variable, 5th edn (London, 1962).Google Scholar
2.Nielsen, N., Handbuch der Theorie der Gamma Fimktion (Leipzig, 1906).Google Scholar
3.Erdélyi, A., Magnus, W., Oberhetinger, F. and Tricomi, E., Higher transcendental functions, Vol. 1 (New York, 1953).Google Scholar
4.Ragab, F. M., New integral representations of the modified Bessel function of the second kind, Mathematics Research Center, University of Wisconsin, 1965.Google Scholar