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A method is given for obtaining series expansions for the coefficients in the double series for the autocorrelation function of the output of a nonlinearity with a signal plus noise as input. Two series are obtained, one in powers and the other in inverse powers of the signal-to-noise ratio. The terms in the series are products of two functions. In these series one function depends on the moments of the signal (or noise) and the other on characteristics of the nonlinearity and the noise (or signal). Differential recursion relationships that simplify evaluation of the nonlinearity-dependent functions are given.