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Certain integral representations for Whittaker functions

Published online by Cambridge University Press:  24 October 2008

Hari Shanker
Hari Shanker
Affiliation:
Anglo-Arabic CollegeDelhi University, India
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Extract

1. Shastri (1) has shown that if and then

But (Goldstein (2))

hence substituting from (1·2) in (1·1) and changing the order of integration, which we suppose to be permissible, we find that if

then

assuming of course that the integrals converge.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 3 , July 1948 , pp. 453 - 455
Copyright
Copyright © Cambridge Philosophical Society 1948

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References

REFERENCES

(1)Shastri, N. A.Proc. Indiana Acad. Sci. 20 (1944), 211–23.CrossRefGoogle Scholar
(2)Goldstein, S.Proc. London Math. Soc. (2), 34 (1932), 103–25.CrossRefGoogle Scholar
(3)Meijer, C. S.Nieuw Arch. Wiskunde, (2), 18 (1934), 35–57.Google Scholar
(4)Erdelyi, A.Proc. Benares Math. Soc. N.S., 1 (1939), 39–53.Google Scholar
(5)Meijer, C. S.Proc. K. Akad. Wet. Amsterdam, 37 (1934), 805–12.Google Scholar
(6)Watson, G. N.The Theory of Bessel-Functions (1922), § 13.21 (8).Google Scholar
(7)Hari, Shanker. J. Indian Math. Soc. 7 (1943), 63–7.Google Scholar