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On the Reduction of Ferrers' Associated Legendre Function

Published online by Cambridge University Press:  20 January 2009

Hrishikesh Sircar
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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.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 1 , Issue 4 , July 1929 , pp. 241 - 243
Copyright
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