Preface
Contents
1 Introduction
2 Moment functionals on P and orthogonal polynomials
2.1 Existence of orthogonal polynomial sequences
2.2 Three-term recurrence relation
2.3 Christoffel–Darboux kernel polynomials
2.4 Polynomials of the first kind and the Stieltjes function
3 Continued fractions
3.1 Continued fractions and orthogonal polynomials
4 Zeros of orthogonal polynomials
4.1 The interlacing property of zeros
5 Gauss quadrature rules
6 Symmetric functionals
6.1 LU factorization
7 Transformations of moment functionals
7.1 Canonical Christoffel transformation
7.2 Canonical Geronimus transformation
7.3 Uvarov transformation
8 Classical orthogonal polynomials
8.1 The linear differential operator and its solutions
8.2 Weight function and inner product
9 Classical functionals
10 Electrostatic interpretation for the zeros of classical orthogonal polynomials
10.1 Equilibrium points on a bounded interval with charged end points
10.2 Equilibrium points on the complex plane: The Bessel case
10.3 Classical orthogonal polynomials and the inverse problem
11 Semiclassical functionals
12 Examples of semiclassical orthogonal polynomials
13 The Askey scheme
13.1 Hahn polynomials
13.2 Jacobi polynomials
13.3 Meixner polynomials
13.4 Krawtchouk polynomials
13.5 Laguerre polynomials
13.6 Bessel polynomials
13.7 Charlier polynomials
13.8 Hermite polynomials
13.9 Limit relations
References
Index