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A Theorem in Operational Calculus and some Integrals involving Legendre, Bessel and E-Functions

Published online by Cambridge University Press:  18 May 2009

C. B. Rathie
C. B. Rathie
Affiliation:
Maharana Bhupal College, Udaipur
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In this paper we prove a theorem in Operational Calculus and use it to evaluate a few infinite integrals involving Legendre, Bessel and E-functions. We write

when

and

when

(2) is a generalisation of (1) as given by Meijer [2] and it reduces to (1) when v = ±½ by virtue of the relation

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 2 , Issue 4 , February 1956 , pp. 173 - 179
Copyright
Copyright © Glasgow Mathematical Journal Trust 1956

References

REFERENCES

(1)MacRobert, T. M., Spherical Harmonics, Methuen (1947).Google Scholar
(2)Meijer, C. S., “Uber eine Erweiterung der Laplace-Transformation”, Proc. Kon. Neder. Akad. van Wetenschappen, (5), 43 (1940).Google Scholar
(3)Ragab, F. M., Proc. Glasg. Math. Assn., Pt. Ill, 1 (1953).Google Scholar
(4)Watson, G. N., Theory of Bessel Functions, (1944).Google Scholar