We introduce a class of partially coherent, Schell-type sources whose degree of coherence is represented by a finite series of complex-valued functions. The significance of implementing such a series is due to the fact that one can manipulate the weighting coefficients of its terms having a computationally trivial linear phase of the degree of coherence for obtaining the radiated beams of the same complexity as could only be previously achieved with analytically intractable nonlinear phases. Our examples illustrate new opportunities for modeling asymmetric coherence gratings and lattices.