Pearson equations for discrete orthogonal polynomials: I. Generalized hypergeometric functions and Toda equations

• Published in: Studies in applied mathematics (Cambridge) Vol. 148; no. 3; pp. 1141 - 1179
• Main Authors: Mañas, Manuel, Fernández‐Irisarri, Itsaso, González‐Hernández, Omar F.
• Format: Journal Article
• Language: English
• Published: Cambridge Blackwell Publishing Ltd 01.04.2022
• Subjects: 3D Nijhoff–Capel discrete Toda equation; Cholesky factorization; contigous relations; Deformation; discrete orthogonal polynomials; generalized hypergeometric functions; Hypergeometric functions; Independent variables; Mathematical analysis; Norms; Pearson equations; Polynomials; Toda hierarchy

The Cholesky factorization of the moment matrix is applied to discrete orthogonal polynomials on the homogeneous lattice. In particular, semiclassical discrete orthogonal polynomials, which are built in terms of a discrete Pearson equation, are studied. The Laguerre–Freud structure semiinfinite matr...