Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-25T16:31:18.274Z Has data issue: false hasContentIssue false

An infinite integral involving Bessel functions and parabolic cylinder functions

Published online by Cambridge University Press:  24 October 2008

R. S. Varma
Affiliation:
Cawnpore

Extract

The object of this paper is to evaluate an infinite integral involving Bessel functions and parabolic cylinder functions. The following two lemmas are required:

Lemma 1.

provided that R(m) > 0.

Type
Research Article
Copyright
Copyright © Cambridge Philosophical Society 1937

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Jeffreys, H., Operational methods in mathematical physics (Cambridge, 1927).Google Scholar
(2)Whittaker, E. T., “On the functions associated with the parabolic cylinder in harmonic analysis”, Proc. Lond. Math. Soc. (1) 35 (1903), 417–27.Google Scholar
(3)Van der Pol, B., “On the operational solution of linear differential equations and an investigation of the properties of these solutions”, Phil. Mag. 8 (1929), 861–98.Google Scholar
(4)Goldstein, S., “Operational representation of Whittaker's confluent hypergeometric function and Weber's parabolic cylinder function”, Proc. Lond. Math. Soc. (2) 34 (1932), 103–25.Google Scholar
(5)Whittaker, E. T. and Watson, G. N., Modern Analysis (4th ed.) (Cambridge, 1927), p. 347.Google Scholar