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Analytical expressions for mutual coupling between slots embedded in a large ground plane are presented and discussed, both for piecewise-sinusoidal and for cosinusoidal field distribution. In the former an exact analytical expression has been found; in the latter various approximations based on Taylor and/or Fourier representation, have been analyzed. One of these approximations extends rigorously an empirical relation recently presented to speed up the time required for the evaluation of mutual coupling. Such expressions are found to be faster to evaluate than numerical integration with comparable error level. This allows the extension of slot array synthesis procedures based on the explicit evaluation of coupling to large arrays even on micro- and minicomputers.