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Integrals involving E-functions

Published online by Cambridge University Press:  18 May 2009

T. M. Macrobert
T. M. Macrobert
Affiliation:
The University Glasgow
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1. Introductory. The following two integrals will be established in § 2.

If m is a positive integer, if p ≧ q + 1 and if R(ar+kt) > 0 (r = 1, 2,…, p, t = 1, 2,…, m),

where co is 1 or e±in according as m is even or odd, the dash denotes that the factor sin (k,–k,)π does not appear and the asterisk that the parameter kt–kt + 1 is omitted. If pp ≧ qthe result holds if the integral is convergent.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 1 , January 1963 , pp. 31 - 33
Copyright
Copyright © Glasgow Mathematical Journal Trust 1963

References

REFERENCES

1.Erdélyi, A., Magnus, W., Oberhettinger, F. and Tricomi, F. G., Higher transcendental functions, Vol. I (New York, 1953).Google Scholar
2.MacRobert, T. M., Functions of a complex variable, 5th edition (London, 1962).Google Scholar
3.Ragab, F. M., Integrals of E-functions expressed in terms of E-functions, Proc. Glasgow Math. Assoc., 1 (1953), 192–195.CrossRefGoogle Scholar