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Published online by Cambridge University Press: 18 May 2009
§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.
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.
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