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XIII.—Some Integrals, with respect to their Degrees, of Associated Legendre Functions

Published online by Cambridge University Press:  15 September 2014

T. M. MacRobert
T. M. MacRobert
Affiliation:
University of Glasgow
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Extract

Little is known regarding the integration of Legendre Functions with respect to their degrees. In this paper several such integrals are evaluated, three different methods being employed. In § 2 proofs are given of a number of formulae which are required later. In § 3 an example is given of the evaluation of an integral by contour integration. The following section contains the proof of a formula of the Fourier Integral type, a special case of which was given in a previous paper (Proc. Roy. Soc. Edin., vol. li, 1931, p. 123). In § 5 an integral is evaluated by employing Fourier's Integral Theorem; while in § 6 other integrals are evaluated by. means of expansions in series.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 54 , 1935 , pp. 135 - 144
Copyright
Copyright © Royal Society of Edinburgh 1935

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