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Infinite integrals involving products of Legendre functions

Published online by Cambridge University Press:  18 May 2009

K. C. Sharma
Affiliation:
Maharana Bhutal CollegeUdaipur
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In this paper we evaluate a few infinite integrals involving products of Legendre functions. The results obtained herein are quite general and include, as particular cases, some known results.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 1957

References

REFERENCES

1.Erdélyi, A., Tables of integral transforms, Vol. I (New York, 1954).Google Scholar
2.Erdélyi, A., Tables of integral transforms, Vol. II (New York, 1954).Google Scholar
3.Erdélyi, A., Higher transcendental functions, Vol. I (New York, 1953).Google Scholar
4.Goldstein, S., Operational representation of Whittaker's confluent hypergeometric function and Weber's parabolic cylinder functions, Proc. London Math. Soc, (2) 34 (1932), 103125.Google Scholar
5.MacRobert, T. M., Some integrals involving Legendre and Bessel functions, Quart. J. Math. (Oxford), (2) 42 (1940), 95100.CrossRefGoogle Scholar
6.MacRobert, T. M., Functions of a complex variable (London, 1954).Google Scholar
7.Meijer, C. S., Uber eine Erweiterung der Laplace-Transformation, Proc. Kon. Nederl. Akad. Wetensch., (5) 43 (1940), 599608.Google Scholar
8.Meijer, C. S., Integraldarstellungen für Whittakersche Funktionen und ihre Produkte, Proc. Nederl. Akad. Wetensch., (5) 44 (1941), 599605.Google Scholar
9.Rathie, C. B., A theorem in operational calculus and some integrals involving Legendre, Bessel and E-functions, Proc. Glasgow Math. Assoc., 2 (1956), 173182.CrossRefGoogle Scholar