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Some series and integrals involving associated Legendre functions (II)

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 paper published recently in these Proceedings, I have proved the formulae

where R(m)>0;

where R(m) > −½; and

where R(m) >− 1. In each case n is unrestricted.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 27 , Issue 3 , July 1931 , pp. 381 - 386
Copyright
Copyright © Cambridge Philosophical Society 1931

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References

REFERENCES

Bailey, W. N., 1; “Some series and integrals involving associated Legendre functions,” Proc. Camb. Phil. Soc. 27 (1931), 184–189.Google 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.Google Scholar
Van der Pol, B., 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