Nonlinear terms produced by passing amplitude-modulated sinusoids through a hair cell transducer function

We derive mathematically the output of Corey and Hudspeth's hair cell transducer function for the following cases: (1) the input is a single carrier whose output is modulated by the sum of two sinusoids; (2) the input is the sum of two carriers, each of which is amplitude-modulated by a single sinusoid. The theoretical results are similar to the results of an experiment in which field potentials were recorded from the human scalp while one ear was stimulated with auditory waveform (1) and with auditory waveform (2) of the cases above.