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Some definite integrals involving Legendre functions

Published online by Cambridge University Press:  24 October 2008

W. N. Bailey
W. N. Bailey
Affiliation:
Trinity College
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Extract

The integral

where n is a positive integer, was obtained recently by Van der Pol by operational methods.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 26 , Issue 4 , October 1930 , pp. 475 - 479
Copyright
Copyright © Cambridge Philosophical Society 1930

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References

* Phil. Mag. 8 (1929), 861–898 (70).CrossRefGoogle Scholar

† See G. N. Watson, Theory of Bessel Functions, § 12·2 (4).

‡ G. N. Watson, loc. cit. § 12·2 (3).

§ G. N. Watson, loc. cit. § 12·21.

* G. N. Watson, loc. cit. § 12·2 (4).

† Bailey, W. N., “Some integrals of Kapteyn's type involving Bessel functions”, Proc. London Math. Soc. (2), 30 (1930), 422–424.CrossRefGoogle Scholar See also Bailey, W. N., “Some definite integrals involving Bessel functions”, Proc. London Math. Soc. (2), 31 (1930), 200–208.Google Scholar

* G. N. Watson, loc. cit. § 5·22 (7).