This paper uses a simple closed-form technique for the computation of the symbol error rate or bit error rate for the performance of coherent M-ary digital modulation schemes over Nakagami-m fading, Rician fading and perturbed by additive white gaussian noise. The expressions for the symbol error probability or bit error probability are simple and include Gauss hypergeometric functions which can be handled using Matlab or Mathematica software packages. The effect of maximal ratio combining diversity method is also considered.