Real Semiclassical Approximation for the Asymptotics of Jacobi Polynomials Given by a Difference Equation

The paper is devoted to constructing the global asymptotics of Jacobi polynomials by the method of “real semiclassics for problems with complex phases,тАЩтАЩ which is based on the study of recurrence relations. The method is based on the semiclassical approximation and the study of the geometry and types of singularities of the arising Lagrangian manifolds. While manifolds with a turning point in whose neighborhood the asymptotics is determined by the Airy function are well studied, the methods for the case in which the asymptotics is determined by the Bessel functions are not so well developed. In this paper, we demonstrate the application of the above-mentioned method in both situations, in particular, we describe the Lagrangian manifold that arises in the second case. DOI 10.1134/S1061920824040162