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Carter, Knapp, and Nuttall  presented a discrete Fourier transform (DFT) method for estimating the magnitude-squared coherence between two zero-mean wide-sense-stationary random processes. This paper shows that a simple Legendre polynomial expression can replace the hypergeometric function used in the probability density function expression of Carter et al.  (see also Fisher  and Goodman ) for the coherence estimate obtained from nonoverlapped DFT's. A standard Legendre polynomial recursion provides a recursive method for evaluating the density expression.