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Some Integrals involving Legendre Functions

Published online by Cambridge University Press:  20 January 2009

W. D. Collins
W. D. Collins
Affiliation:
Department of Mathematics, King's College, Newcastle upon Tyne
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In this note generalisations of certain integrals involving Legendre functions including the Mehler-Dirichlet integral for Legendre functions of the first kind are given, these new results expressing associated Legendre functions of the first or second kinds as integrals involving corresponding functions of the same degree but different order. These integrals appear to be analogous to Sonine's integral in the theory of Bessel functions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 11 , Issue 3 , May 1959 , pp. 161 - 165
Copyright
Copyright © Edinburgh Mathematical Society 1959

References

REFERENCES

Bateman Manuscript Projeot, Higher Transcendental Functions, vol. I (McGraw-Hill, 1953).Google Scholar
Fock, V. A., C.R. (Dolclady) Acad. Sci. U.R.S.S. (N.S.) (1943), pp. 253–256.Google Scholar