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Some properties of Legendre functions

Published online by Cambridge University Press:  24 October 2008

J. C. Cooke
J. C. Cooke
Affiliation:
University of MalayaSingapore
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Extract

Nicholson (3) stated that the Legendre functions of the second kind, Qn(x), are orthogonal between − 1 and 1. This is incorrect in general, and one purpose of this paper is to give the correct value of

when m ╪ n. Nicholson's value of the integral when m = n, namely,

is correct.

Type
Research Notes
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 1 , January 1953 , pp. 162 - 164
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

(1)Cossar, J. and Erdélyi, A.Dictionary of Laplace transforms, part 2B (Admiralty Computing Service, London, 1945), p. VI68.Google Scholar
(2)Magnus, W. and Oberhettinger, F.Formulas and theorems for the special functions of mathematical physics (New York, 1949), p. 63.Google Scholar
(3)Nicholson, J. W.Phil. Mag. (6), 43 (1922), 1.CrossRefGoogle Scholar
(4)Nicholson, J. W.Philos. Trans. A, 224 (1924), 320.Google Scholar