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On the Reduction of Ferrers' Associated Legendre Function
Published online by Cambridge University Press: 20 January 2009
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Introduction. In the present paper a formula will be obtained to express a Ferrers' Associated Legendre Function of any integral degree and order as a sum of a finite number of Associated Legendre Functions of an order reduced by an even number. When the order is reduced by unity, an infinite series of the functions of reduced order is required. Thus a Ferrers' function can be expressed as the sum of a finite or infinite number of zonal harmonics according as the order of the function is even or odd.
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- Copyright © Edinburgh Mathematical Society 1929
References
page 242 note 1 Collected Scientific Papers, 2, 412. Cf. also 2, 376.Google Scholar
page 243 note 1 Todhunter, . The functions of Laplace, Lame and Bessel, p. 114. Also Crelle, 56.Google Scholar
page 243 note 2 Adams, . Collected Scientific Papers, 2, 395, the quotation is given in an altered form. There is also another equivalent expression of order n-p.Google Scholar
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