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On Neumann's Formula for the Legendre Functions

Published online by Cambridge University Press:  18 May 2009

T. M. Macrobert
T. M. Macrobert
Affiliation:
University of Glasgow
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§1. Introductory. The formula

where w is zero or a positive integer and | ζ | > 1, was given by F. E. Neumann “Crelle's Journal, XXXVII (1848), p. 24”. In § 2 of this paper some related formulae are given; the extension to the case when n is not integral is dealt with in § 3; while in § 4 the corresponding formulae for the Associated Legendre Functions when the sum of the degree and the order is a positive integer are established.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 1 , Issue 1 , January 1952 , pp. 10 - 12
Copyright
Copyright © Glasgow Mathematical Journal Trust 1952

References

page 11 note * Cf. Phil. Mag., Ser. 7, XXXV (1944), p. 673–6Google Scholar.

page 12 note * Cf. Gormley, P. G., Journal of the London Math. Soc., IX. (1933), 149Google Scholar.