Asymptotics of polynomials orthogonal with respect to a generalized Freud weight with application to special function solutions of Painlevé‐IV
Copyright policy )Asymptotics of polynomials orthogonal with respect to a generalized Freud weight with application to special function solutions of Painlevé‐IV
AbstractWe obtain asymptotics of polynomials satisfying the orthogonality relations where the complex parameter is in the so‐called two‐cut region. As an application, we deduce asymptotic formulas for certain families of solutions of Painlevé‐IV which are indexed by a nonnegative integer and can be written in terms of parabolic cylinder functions. The proofs are based on the characterization of orthogonal polynomials in terms of a Riemann–Hilbert problem and the Deift–Zhou nonlinear steepest descent method.
Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain, Primary: 34M55, 33C47, Secondary: 15B52, 30E15, 34E05, 34M50, Painlevé-type functions, Riemann-Hilbert analysis, Mathematics - Complex Variables, FOS: Physical sciences, Other special orthogonal polynomials and functions, Mathematical Physics (math-ph), non-Hermitian orthogonal polynomials, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Painlevé IV equation, Mathematics - Classical Analysis and ODEs, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Complex Variables (math.CV), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mathematical Physics
Inverse problems (Riemann-Hilbert, inverse differential Galois, etc.) for ordinary differential equations in the complex domain, Primary: 34M55, 33C47, Secondary: 15B52, 30E15, 34E05, 34M50, Painlevé-type functions, Riemann-Hilbert analysis, Mathematics - Complex Variables, FOS: Physical sciences, Other special orthogonal polynomials and functions, Mathematical Physics (math-ph), non-Hermitian orthogonal polynomials, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Painlevé IV equation, Mathematics - Classical Analysis and ODEs, Painlevé and other special ordinary differential equations in the complex domain; classification, hierarchies, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Complex Variables (math.CV), Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, Mathematical Physics
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