The equations for the unbounded metalog distribution are shown below. These are reproduced from The Metalog Distributions, Section 3.3. The first ten terms of these equations are implemented in "Unbounded Metalog" and "ELD Unbounded Metalog" Excel workbooks.
The unbounded-metalog feasibility condition, is mn(y) > 0 for all y in the open interval (0,1). See The Metalog Distributions, Section 3.3, Equation (10) for more information.