Classical Orthogonal Polynomials of a Discrete Variable [Paperback]

1. Classical Orthogonal Polynomials.- 1.1 An Equation of Hypergeometric Type.- 1.2 Polynomials of Hypergeometric Type and Their Derivatives. The Rodrigues Formula.- 1.3 The Orthogonality Property.- 1.4 The Jacobi, Laguerre, and Hermite Polynomials.- 1.4.1 Classification of Polynomials.- 1.4.2 General Properties of Orthogonal Polynomials.- 1.5 Classical Orthogonal Polynomials as Eigenfunctions of Some Eigenvalue Problems.- 2. Classical Orthogonal Polynomials of a Discrete Variable.- 2.1 The Difference Equation of Hypergeometric Type.- 2.2 Finite Difference Analogs of Polynomials of Hypergeometric Type and of Their Derivatives. The Rodrigues Type Formula.- 2.3 The Orthogonality Property.- 2.4 The Hahn, Chebyshev, Meixner, Kravchuk, and Charlier Polynomials.- 2.5 Calculation of Main Characteristics.- 2.6 Asymptotic Properties. Connection with the Jacobi, Laguerre, and Hermite Polynomials.- 2.7 Representation in Terms of Generalized Hypergeometric Functions.- 3. Classical Orthogonal Polynomials of a Discrete Variable on Nonuniform Lattices.- 3.1 The Difference Equation of Hypergeometric Type on a Nonuniform Lattice.- 3.2 The Difference Analogs of Hypergeometric Type Polynomials. The Rodrigues Formula.- 3.3 The Orthogonality Property.- 3.4 Classification of Lattices.- 3.5 Classification of Polynomial Systems on Linear and Quadratic Lattices. The Racah and the Dual Hahn Polynomials.- 3.6 q-Analogs of Polynomials Orthogonal on Linear and Quadratic Lattices.- 3.6.1 The q-Analogs of the Hahn, Meixner, Kravchuk, and Charlier Polynomials on the Lattices x(s) = exp(2?s) and x(s) = sinh(2?s).- 3.6.2 The q-Analogs of the Racah and Dual Hahn Polynomials on the Lattices x(s) = cosh(2?s) and x(s) = cos(2?s).- 3.6.3 Tables of Basic Data for q-Analogs.- 3.7 Calculation of the Leading Coefficients and Squared Norms. Tables of Data.- 3.8 Asymptotic Properties of the Racah and Dual Hahn Polynomials.- 3.9 Construction of Some Orthogonal Polynomials on Nonuniform Lattices by Means of the DlC<