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An Integral over the Interior of a Simplex

Published online by Cambridge University Press:  20 January 2009

Henry Jack
Henry Jack
Affiliation:
Queen's College, Dundee
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If f(z) is analytic in a suitable domain, it is shown how the integral of f(α1x1+…+αnxn) over the interior of a simplex may be reduced to the evaluation of a contour integral, in fact to an exercise in partial fractions.

The contour integral is expressed in two ways, according as the simplex is given in terms of its vertices or faces.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 13 , Issue 2 , December 1962 , pp. 167 - 171
Copyright
Copyright © Edinburgh Mathematical Society 1962

References

(1) Jack, H. and Macbeath, A. M., The volume of a certain set of matrices, Proc. Cambridge Phil. Soc. 55 (1959), 213–223.CrossRefGoogle Scholar
(2) Sommerville, D. M. Y., An introduction to the geometry of N dimensions (London, 1929).Google Scholar
(3) Turnbull, H. W., Note on partial fractions and determinants, Proc. Edinburgh Math. Soc. (2) 1 (1927–1929), 49–54.CrossRefGoogle Scholar