Mathematical Proceedings of the Cambridge Philosophical Society

Research Article

An integral which occurs in statistics

Mr A. E. Inghama1

a1 King's College

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

S0305004100011075eqnU1

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

(Received February 13 1933)

(Accepted March 06 1933)