In the present work, simple closed-form series solutions for the average error rate of several coherent modulation schemes such as, binary phase shift keying (BPSK), binary frequency shift keying (BFSK), differential binary phase shift keying (DBPSK), quadrature phase shift keying (QPSK), offset-QPSK, minimum shift keying (MSK), and square M-ary quadrature amplitude modulation (M-QAM), operating over frequency non-selective slow Rician fading channel and corrupted by additive white Gaussian noise (AWGN) are derived. Further, to improve the link quality, receiver antenna space diversity is considered, where multiple independent and identically distributed (i.i.d.) as well as uncorrelated signal replicas are combined before successive demodulation. The proposed linear predetection combiner follows optimum maximal ratio combining (MRC) algorithm. Starting from a novel unified expression of conditional error probability the error rates are analysed using probability density function (pdf) based approach. The derived end expressions, consisting of rapidly converging infinite series summations of Gauss hypergeometric function, are accurate, free from any numerical integration and general enough, as it encompasses as special situations, some cases of non-diversity, non-fading AWGN and Rayleigh fading. Symbol or, bit error probabilities (SEP/BEP) are graphically displayed against signal to noise ratio (SNR) per bit per channel for all the digital modulation schemes stated above with different values of diversity order L and varying values of the channel specular-to-scatter ratio or, the Rician parameter K, as found from the measured statistics of mobile and indoor wireless channels. In addition, to examine the dependence of error rate performance of M-QAM on the constellation size M, numerical results are plotted for various values of M. Selected simulation results are also provided to verify the analytical deductions. The series solutions presented in current text realize a trade-off between precision and complexity and offers valuable insight into the performance evaluation over a fading channel in a unified manner.