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Recently pi/4 shifted differential quadrature phase shift keying (pi/4-DQPSK) modulation has attracted much attention as it is used for high-capacity code division multiple access (CDMA) based digital cellular systems. One of the major reason behind this is the provision for differential detection which allows production of low complexity mobile units. In this paper, we present analytical expressions for bit error rate (BER) of pi/4-DQPSK modulation with L-branch selection combining (SC) diversity in Nakagami-m fading channels perturbed by additive white Gaussian noise (AWGN). The derived end expressions are in closed form and contain finite series of Gaussian hypergeometric function. This makes evaluation of error rates much straightforward compared to earlier approaches that required single or, even double numerical integration. Some special instances such as the non-diversity case and Rayleigh fading case are also investigated and plotted alongwith the main findings. The results are however limited to integer values of fading severity parameter m.