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On the function

Published online by Cambridge University Press:  24 October 2008

A. S. Meligy  and
E. M. EL Gazzy
A. S. Meligy
Affiliation:
Faculty of Science, University of Alexandria, Alexandria, Egypt
E. M. EL Gazzy
Affiliation:
Faculty of Science, University of Alexandria, Alexandria, Egypt
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Extract

In a previous paper (3) one of us reported an expansion for the exponential integral

in terms of Bessel functions. In this note, we shall obtain the more general formula

where n is any positive integer, γ is Euler's constant and

It reduces to that in (3) when n = 1.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 59 , Issue 4 , October 1963 , pp. 735 - 737
Copyright
Copyright © Cambridge Philosophical Society 1963

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References

REFERENCES

(1)Bailey, W. N.Generalized hypergeometric series (Cambridge, 1935).Google Scholar
(2)Meligy, A. S.Quart. J. Math. Oxford Ser. (2), 10 (1959), 202.CrossRefGoogle Scholar
(3)Meligy, A. S.Proc. Cambridge Philos. Soc. 56 (1960), 233.CrossRefGoogle Scholar
(4)Slater, L. J.Confluent hypergeometric functions (Cambridge, 1960).Google Scholar
(5)Whittaker, E. T. and Watson, G. N.Modern analysis, 4th ed. (Cambridge, 1927).Google Scholar