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  • Mathematical Proceedings of the Cambridge Philosophical Society, Volume 29, Issue 2
  • May 1933, pp. 271-276

An integral which occurs in statistics

  • A. E. Ingham (a1)
  • DOI:
  • Published online: 24 October 2008

1. In this note we give a direct evaluation of the integral

whose value has been inferred from the theory of statistics. Here A = Ap = (αμν) and C = Cp = (Cμν) are real symmetrical matrices, of which A is positive definite; there are ½ p (p + 1) independent variables of integration tμν (1 ≤ μ ≤ ν ≤ p), and tμν is written also as tνμ for symmetry of notation; in the summation ∑ the variables μ, ν run independently from 1 to p; k is a real number. A word of explanation is necessary with regard to the determination of the power |AiT|k. Since A is positive definite and T real and symmetric, the roots of the equation

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J. Wishart and M. S. Bartlett , Proc. Camb. Philos. Soc. 29 (1933), 260270

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