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Some series and integrals involving associated 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

1. In a recent paper I have given some definite integrals involving Legendre functions which, as a limiting case, give known results involving Bessel functions. In another paper I have shown how some integrals involving Bessel functions can be obtained from Bateman's integral

and the well-known expansion

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 27 , Issue 2 , April 1931 , pp. 184 - 189
Copyright
Copyright © Cambridge Philosophical Society 1931

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References

REFERENCES

Bailey, W. N., 1; “Some definite integrals involving Legendre functions,” Proc. Camb. Phil. Soc. 26 (1930), 475–479.CrossRefGoogle Scholar
Bailey, W. N., 2; “Some definite integrals involving Bessel functions,” Proc. London Math. Soc. (2), 31 (1930), 200–208.Google Scholar
Bailey, W. N., 3; “Some integrals of Kapteyn's type involving Bessel functions,” Proc. London Math. Soc. (2), 30 (1930), 422–424.CrossRefGoogle Scholar
Proudman, J., 1; “Note on an expansion of Neumann type in a special class of hypergeometric functions,” Journal London Math. Soc. 1 (1926), 231–233.CrossRefGoogle Scholar
Pol, B. Van der, 1; “On the operational solution of linear differential equations and an investigation of the properties of these solutions,” Phil. Mag. 8 (1929), 861–898.Google Scholar
Watson, G. N., 1; Theory of Bessel Functions.Google Scholar