This paper presents unified and accurate performance analysis of multiple dual-hop, non-generative relays in cooperative wireless communication systems over independent and non-identical Nakagami-m fading channels with arbitrary fading parameters. The performance is studied in terms of the average symbol error probability for various coherent modulation schemes. Our proposed moment generating function based analytical framework is also sufficiently general to compress all types of coherent, differentially-coherent and non-coherent digital modulation schemes. The accuracy of the proposed method is verified by simulation and compared to the exact and approximate solutions. The proposed mathematical analysis is complemented by numerical results for average symbol error probability; including the effect of fading severity of the channel, number of acting relays, existence of the direct path between the source and the destination, and transmitted signal-to-noise ratio. Moreover, the numerical results study the effect of fading parameters and the number of cooperative relays on the performance of the average symbol error probability.