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A generalization of an early multivariate integral

Published online by Cambridge University Press:  20 January 2009

Henry Jack
Henry Jack
Affiliation:
The University, Dundee
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Earlier this year Professor W. L. Edge drew my attention to the paper (1). Since Black probably wrote his paper about 1890, the integral he considered must have been one of the earliest n-variate integrals to be evaluated. The present paper generalizes Black's result from a column vector as variate to a rectangular matrix—his integral is the case p = m = k = 1 of the integral J below.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 2 , December 1972 , pp. 125 - 128
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

(1) Black, A., Reduction of a certain multiple integral, Trans. Cambridge Philos. Soc. 16 (1898), 219–225.Google Scholar
(2) Cramer, H., Mathematical methods of statistics (Princeton, 1946).Google Scholar
(3) Ferrar, W. L., Algebra (Oxford, 1941).Google Scholar
(4) Jack, H., Jacobians of transformation involving orthogonal matrices, Proc. Roy. Soc. Edinburgh Sect. A 67 (1966), 81–103.Google Scholar
(5) Jack, H., A Class of symmetric polynomials with a parameter, Proc. Roy. Soc. Edinburgh Sect. A 69 (1970), 1–18.Google Scholar
(6) Turnbull, H. W. and Aitken, A. C., Theory of canonical matrices (Blackie and Son, 1965).Google Scholar