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Simple analytic expressions are presented for the two‐dimensional electron gas density and the drain current in a high‐electron mobility transistor. These compact expressions, which are based on the Lambert W‐function, are continuous over the entire range of interest. The analytic differentiation or integration of the drain current can also be expressed in terms of the Lambert W‐function. The expression for carrier density is in close agreement with rigorous numerical calculations while the expression for the drain current presents reasonable agreement with measurements.