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We derive the exact theoretical symbol error rate (SER) of M-ary phase-shift keying (M-PSK), differentially encoded M-ary PSK (DE-M-PSK) and M-ary quadrature amplitude modulation (M-QAM), for EGC with two correlated diversity branches in Nakagami-m fading. The starting point is the derivation of the probability density function (pdf) of the sum of two correlated Nakagami-m variables, for which no closed-form expression was previously available in the communications literature. Several novel expressions are then obtained, either in the form of a single-dimensional integral, or in closed-form as infinite series summations. Some closed-form solutions for the SER of dual-branch MRC can also be derived by using an alternative expression for the pdf of the sum of the squares of two correlated Nakagami-m variables.