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Published online by Cambridge University Press: 15 September 2014
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.
page 20 note * Cf. Whipple, F. J. W., Proc. Lond. Math. Soc., vol. xvi, 1917, p. 308.Google Scholar
