Summary: Many orthogonal polynomials \(u(n,z)\) (\(n\) is the number of the polynomial, \(z\) is its argument), for example, the Chebyshev, Hermite, Laguerre, Legendre, and other polynomials, are determined by recurrence relations (or finite-difference equations) of the second order. For large numbers \(n\), they are approximated by exponential, trigonometric, or special functions of a compound argument. For example, Hermite polynomials are approximated by the Plancherel-Rotach formulas, in which the special function is Ai, the Airy function, the Legendre polynomials are approximated by the zero-order Bessel function, etc. In the paper, an approach is developed for finding asymptotics of this type, which are uniform in this case (and unified) with respect to the variable \(z\). The approach is based on the passage from discrete equations to continuous pseudodifferential equations and the subsequent application of the semiclassical approximation to these equations with complex phases. This is a further development of the considerations proposed in the papers of A. I. Aptekarev et al. [“Asymptotics of the Plancherel-Rotach type for jointly orthogonal Herite polynomials and recurrent relations”, Izv. Math. (to appear)], A. I. Aptekarev and D. N. Tulyakov [Sb. Math. 205, No. 12, 1696–1719 (2014; Zbl 1317.39001); translation from Mat. Sb. 205, No. 12, 17–40 (2014)], D. N. Tulyakov [ibid. 201, No. 9, 1355–1402 (2010; Zbl 1242.39002); translation from Mat. Sb. 201, No. 9, 111–158 (2010)] devoted to asymptotics of the Plancherel-Rotach type for Hermite polynomials and a subclass of Hermite type orthogonal polynomials with multiple indices.