An Introduction to Orthogonal Polynomials

a₁ Al-Salam an(x An+1 b₁ Bessel polynomials c₁ Carlitz chain sequence Charlier polynomials Chihara classical orthogonal polynomials Cn+1 continued fraction converges COROLLARY corresponding monic defined denote determined differential equation distribution function Erdélyi finite follows Gauss quadrature formula Hamburger moment problem hence Hermite polynomials I-Ex I-Theorem integral interval of orthogonality Jacobi polynomials k₁ Laguerre polynomials leading coefficient Legendre polynomials Let P(x limit point m₁ Math maximal parameter sequence Meixner polynomials monic OPS non-decreasing obtain OPS with respect orthogonal polynomials orthogonality relation orthonormal polynomial P₁(x Po(x Pollaczek polynomial of degree polynomial sequence positive-definite positive-definite moment functional positive-definite OPS Prove quasi-definite quasi-orthogonal polynomial real numbers recurrence formula satisfy Show spectrum Stieltjes-Wigert polynomials supporting set symmetric Szegö Tchebichef polynomials Theorem 3.2 theory true interval Wall polynomials weight function x₁ zeros of P(x η₁ λη λη+1 μη ξι