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In this paper, we provide a complete Plancherel-Rotach asymptotic analysis ofpolynomials that satisfy a second-order difference equation with linearcoefficients. According to the signs of the parameters, we classify thedifference equations into six cases and derive explicit asymptotic formulas ofthe polynomials in the outer and oscillatory regions, respectively. It isremarkable that the zero distributions of the polynomials may locate on theimaginary line or even on a sideways Y-shape curve in some cases.

Plancherel-Rotach Asymptotics of Second-Order Difference Equations with Linear Coefficients