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On certain new connections between Legendre and Bessel Functions
Published online by Cambridge University Press: 20 January 2009
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Let n be a positive integer. Then we know that, if m>– 1,
Consider the integral
which is equal to
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- Copyright © Edinburgh Mathematical Society 1935
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page 111 note 1 Equation (1) follows at once by putting x = 1 – 2y2, using Rodrigues' formula for P n(x), and integrating n times by parts. CfCooke, , Proc. London Math. Soc., 23 (1924), xix, equ. (3).Google Scholar
page 111 note 2 The process of arrangement and term by term integration can be easily justified.
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