2015/05/31 by Alejandro Arceo, Edmundo J. Huertas, Francisco Marcellán · 8 citations
Mathematics · Physics and Astronomy · #Action (physics) #Fractional Differential Equations Solutions #Logarithm #Mathematical analysis #Mathematical functions and polynomials #Mathematical physics #Mathematics #Monic polynomial #Nonlinear Waves and Solitons #Orthogonal polynomials #Physics #Polynomial #Pure mathematics #Quantum mechanics #Quartic function #math.CA #msc:33C45
paper · pdf · doi:10.1016/j.amc.2016.01.048
published in Applied Mathematics and Computation 281, 102-120 (Elsevier BV) · 27 pages, 1 Figure, accepted for publication in Applied Mathematics and Computation, 2016
arxiv created 2016/01/19 · openalex publication_date 2016/02/16 · arxiv updated 2022/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this contribution we consider sequences of monic polynomials orthogonal with respect to the standard Freud-like inner product involving a quartic potential ⟨ p,q⟩M=∫ℝp(x)q(x)e^-x4+2tx2dx+Mp(0)q(0). We analyze some properties of these polynomials, such as the ladder operators and the holonomic equation that they satisfy and, as an application, we give an electrostatic interpretation of their zero distribution in terms of a logarithmic potential interaction under the action of an external field. It is also shown that the coefficients of their three term recurrence relation satisfy a nonlinear difference string equation. Finally, an equation of motion for their zeros in terms of their dependence on t is given.