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On Integral Transform Pairs Arising from Second Order Differential Equations

Published online by Cambridge University Press:  20 January 2009

A. McD. Mercer
A. McD. Mercer
Affiliation:
The Queen's University, Belfast
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We present in this paper a straight-forward method of deducing integral transform pairs directly from second order differential equations. In (1) this subject has been very thoroughly treated and in view of this we believe that the method described here has its greatest justification in its simplicity.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 1 , June 1962 , pp. 63 - 68
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

REFERENCES

(1) Titchmarsh, E. C., Eigenfunction Expansions (Oxford University Press, London, 1946).Google Scholar
(2) Bromwich, T. J. I'A., Theory of Infinite Series (1926).Google Scholar
(3) Higher Transcendental Functions, The Bateman Manuscript Project, Vol. 2, McGraw-Hill (1953).Google Scholar
(4) Kontorovich, M. J. and Lebedev, N. N., J. Exper. Theor. Phys. U.S.S.R., 8 (1938), 1192–1206.Google Scholar