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On certain new connections between Legendre and Bessel Functions

Published online by Cambridge University Press:  20 January 2009

S. C. Mitra
S. C. Mitra
Affiliation:
Dacca, India.
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Let n be a positive integer. Then we know that, if m>– 1,

Consider the integral

which is equal to

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 4 , Issue 3 , August 1935 , pp. 111
Copyright
Copyright © Edinburgh Mathematical Society 1935

References

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.