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We give a systematic study of q-algebraic equations. The questions ofexistence, uniqueness and regularity of the solutions are solved in the spaceof grid-based Hahn series. The regularity is understood in terms of asymptoticbehavior of coefficients, and is the main focus of this work. The results andalgorithms are illustrated by many examples.

q-Algebraic Equations, their power series solutions, and the asymptotic behavior of their coefficients