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Note on the relations between series equations and integral equations

Published online by Cambridge University Press:  24 October 2008

A. A. Ashour
A. A. Ashour
Affiliation:
High Altitude Observatory, Boulder, Colorado (On leave from the Applied Mathematics Department, Cairo University, Cairo, Egypt)
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Extract

Williams ((3)) has transformed certain series equations in Legendre functions to Bessel integral equations; his main result being that if

then

and vice versa. (Here, n is written for Williams's n + m. The coefficients an are related to Williams's An by a factor. There is an extra factor 2 in equation (7) in Williams's paper which appears to be an error.)

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 61 , Issue 3 , July 1965 , pp. 695 - 696
Copyright
Copyright © Cambridge Philosophical Society 1965

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References

(1)Ashour, A. A.Proc. London Math. Soc. (3) 15 (1965) (to appear).Google Scholar
(2)Noble, B.Electromagnetic Waves (Ed. Langer, Rudolph E.) (Univ. of Wisconsin, 1962).Google Scholar
(3)Williams, W. E.Proc. Cambridge Philos. Soc. 59 (1963), 731–734.CrossRefGoogle Scholar