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We study solutions of a transcendental equation for the complex chemicalpotential at which a random-matrix QCD model can undergo a phase transition atzero mass. An explicit solution is obtained in terms of the Lambert W function.We also provide a closed form expression for a QCD random matrix modelpartition function, as a sum of Laguerre polynomials, for complex chemicalpotential and non-zero mass.

The Lambert W Function, Laguerre Polynomials, and the Zeros of the QCD Partition Function