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On the application of the operational calculus to the expansion of a function in a series of Legendre's functions of the second kind
Published online by Cambridge University Press: 20 January 2009
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In the present note we shall obtain the expansion in a series of Legendre functions of the second kind of an integral function φ (ω) represented by Laplace's integral
where f (x) is an analytic function of x, regular in the circle
where an are constants and qn (ω) = in+1Qn (iω).
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- Research Article
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- Copyright © Edinburgh Mathematical Society 1942
References
1 Watson, , Theory of Hessel functions (Cambridge, 1922), § 16, 11 (3).Google Scholar
2 Nicholson, , “Electrification of parallel circular discs.” Phil. Trans. Royal Soc. (A), 224 (1924), 315.CrossRefGoogle Scholar
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