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Optimum combining (OC) is a powerful means for combatting co-channel interference. Its performance, however, is difficult to analyze. The prevailing methodology in current use is to neglect the influence of additive white Gaussian noise (AWGN). Inclusion of AWGN into the analysis usually leads to mathematical intractability, except for some extreme cases. In this letter, we formulate the problem in the framework of hypergeometric functions, so that their good properties can be exploited to enable the analysis to account for the influence of AWGN and co-channel interference simultaneously. We obtain closed-form solutions to the characteristic function (CHF) of the signal-to-interference-plus-noise ratio at the OC output for three important operational scenarios in Rayleigh fading, although the general solution still needs further effort to simplify. The assumptions made here are that both signal and interferers suffer from Rayleigh fading, and the number of interferers is not less than the number of antennas. The use of resulting CHF formulas is illustrated through their application to the bit-error and outage performance evaluation of OC.