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The Hankel transform of Whittaker's function Wk, m(z)

Published online by Cambridge University Press:  24 October 2008

A. Erdélyi
A. Erdélyi
Affiliation:
Brno, Czechoslovakia
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Extract

The Hankel transform of a function x−½νf(x) can be determined by the help of the following rule, obtained for ν = 0, 1 by B. van der Pol and K. Niessen(1), for positive integral values of ν by K. Niessen(2), and for arbitrary values of ν, [R(ν) > − 1], by F. Tricomi(3). If*

F(p) ≒ f(x),

then

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 34 , Issue 1 , January 1938 , pp. 28 - 29
Copyright
Copyright © Cambridge Philosophical Society 1938

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References

REFERENCES

(1)van der Pol, B. and Niessen, K., Phil. Mag. 13 (1932), 537.CrossRefGoogle Scholar
(2)Niessen, K., Phil. Mag. 20 (1935), 977, equation (1).CrossRefGoogle Scholar
(3)Tricomi, F., Rend. dei Lincei, 22 (1935), 564, § 3.Google Scholar
(4)Whittaker, E. T. and Watson, G. N., Modern analysis, 4th ed. (Cambridge, 1927), chapter 16.Google Scholar
(5)Goldstein, S., Proc. London Math. Soc. (2), 34 (1932), 103, equation (80). See also Erdélyi A., Math. Zeitschrift, 42 (1936), 125, equation (2, 7).CrossRefGoogle Scholar
(6)Varma, R. S., Proc. Cambridge Phil. Soc. 33 (1937), 210.CrossRefGoogle Scholar