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II.—Some Formulæ for the Associated Legendre Functions of the Second Kind; with corresponding Formulæ for the Bessel Functions

Published online by Cambridge University Press:  15 September 2014

T. M. MacRobert
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Extract

In two former papers (Proc. Roy. Soc. Edin., vol. liv, 1934, pp. 135–144; vol. lv, 1935, pp. 85–90) a number of integrals and series, involving Associated Legendre Functions of the First Kind regarded as functions of their degrees, were evaluated. In this paper similar integrals and series for the Associated Legendre Functions of the Second Kind, and also for Bessel Functions, are discussed. The latter are deduced from Bessel's Integral in its generalised form and from the corresponding integral for the Modified Bessel Function of the First Kind; the former from an analogous formula for the Associated Legendre Functions of the Second Kind.

Type
Proceedings
Information
Proceedings of the Royal Society of Edinburgh , Volume 57 , 1938 , pp. 19 - 25
Copyright
Copyright © Royal Society of Edinburgh 1938

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References

page 20 note * Cf. Whipple, F. J. W., Proc. Lond. Math. Soc., vol. xvi, 1917, p. 308.Google Scholar