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A generalization of Sonine's first finite integral

Published online by Cambridge University Press:  18 May 2009

C. J. Tranter
C. J. Tranter
Affiliation:
Royal Military College of ScienceShrivenham
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In this note I show that

where Jdenotes the Bessel function of the first kind of the orders and arguments indicated, n = 0, 1, 2, 3, … and the real parts of both μand v exceed — 1. This is a generalization of Sonine's first finite integral [1, p. 373] to which it reduces in the special case n = 0.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 6 , Issue 2 , July 1963 , pp. 97 - 98
Copyright
Copyright © Glasgow Mathematical Journal Trust 1963

References

REFERENCES

1.Watson, G. N., Theory of Bessel functions (Cambridge, 1944).Google Scholar
2.Magnus, W. and Oberhettinger, F. (translated by Wermer, J.), Special functions of mathematical physics (New York, 1949).Google Scholar
3.Tranter, C. J., Integral transforms in mathematical physics (Methuen, 1956).Google Scholar