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New types of factorizable equations

Published online by Cambridge University Press:  24 October 2008

Mayer Humi
Mayer Humi
Affiliation:
Department of Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel
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Abstract

By a generalization of the Infeld-Hull Factorization Kernels we find it possible to factorize a wide family of second-order ordinary differential equations at specified points of their spectrum.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 68 , Issue 2 , September 1970 , pp. 439 - 446
Copyright
Copyright © Cambridge Philosophical Society 1970

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References

NOTES AND REFERENCES

(1)Infeld, L. and Hull, T. E.Rev. Modern Phys. 23 (1951), 21.CrossRefGoogle Scholar
(2)Kaufman, B. J.Mathematical Phys. 7 (1966), 447.CrossRefGoogle Scholar
(3)Miller, W. Jr. Memoirs of Amer. Math. Soc. no. 50 (1964).Google Scholar
(4)Miller, W. Jr. J. Math. Mech. 17 (1968), 1143.Google Scholar
(5) It is to be remarked that y(λ, m ± 1) might satisfy different boundary conditions other than those of y(λ, m). However, this is not a difficulty, since once a solution of a second-order equation is found the second can be found by quadratures.Google Scholar
(7)Luke, Y. L.The special functions and their approximations (Academic Press, New York, 1969).Google Scholar