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A Generalisation of Dirichlct's Multiple Integral

Published online by Cambridge University Press:  31 October 2008

I. J. Good
I. J. Good
Affiliation:
131 Cheviot Gardens, London, N.W.2.
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The purpose of this note is to generalise the Dirichlet-Liouville formula which expresses a certain type of multiple integral in terms of a single integral. In our formula the multiple integral will involve several arbitrary functions instead of only one, and it will be expressed as a product of single integrals.

Type
Research Article
Information
Edinburgh Mathematical Notes , Volume 38 , January 1952 , pp. 7 - 8
Copyright
Copyright © Edinburgh Mathematical Society 1952

References

1 See, for example, Meyer, G. F., Vorlesungen über die Theorie der bestimmten Integrale (Leipzig, 1871), 566et seq.Google Scholar; or Whittaker, E. T. and Watson, G. N., Modern Analysis (4th edn., Cambridge, 1935)Google Scholar, section 12.5; or Jeffreys, H. and Jeffreys, B. S., Methods of Mathematical Physics (Cambridge, 1946)Google Scholar, section 15.08; or Mordell, L. J., “Dirichlet's integrals,” Edin. Math. Notes, No. 34 (1944), 15–17.CrossRefGoogle Scholar