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Integrals Involving E-Functions and Modified Bessel Functions of the Second Kind

Published online by Cambridge University Press:  18 May 2009

F. M. Ragab
F. M. Ragab
Affiliation:
University of Glasgow and Faculty of Science, Ibrahim University, Cairo
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The two following formulae are to be established.

If R (m ± n) > 0, | amp z | < π,

If p ≧ q + 1, R(k ± n + 2αr) > 0, r = 1, 2, …, p, | amp z | < π,

For other values of p and q the formula holds if the integral is convergent.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 2 , Issue 1 , April 1954 , pp. 52 - 56
Copyright
Copyright © Glasgow Mathematical Journal Trust 1954

References

(1)Gray, Mathews and MacRobert, , Bessel Functions, p. 66.Google Scholar
(2)MacRobert, T. M., Proc. Olasg. Math. Ass., 1, 191 (1953).Google Scholar
(3)MacRobert, T. M., Functions of a Complex Variable (3rd ed., London, 1946), formulae (21), (22), (23), pp. 352, 353.Google Scholar
(4)MacRobert, T. M., Proc. Glasg. Math. Ass., 1, 187 (1953).CrossRefGoogle Scholar