## An Introduction to Orthogonal PolynomialsAssuming no further prerequisites than a first undergraduate course in real analysis, this concise introduction covers general elementary theory related to orthogonal polynomials. It includes necessary background material of the type not usually found in the standard mathematics curriculum. Suitable for advanced undergraduate and graduate courses, it is also appropriate for independent study. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. Numerous examples and exercises, an extensive bibliography, and a table of recurrence formulas supplement the text. |

### Other editions - View all

### Common terms and phrases

a₁ Al-Salam Amer b₁ b₂ Bessel polynomials bounded Carlitz chain sequence Charlier polynomials Chihara class of orthogonal 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 inequality integral interval of orthogonality Jacobi polynomials Karlin kernel polynomials Laguerre polynomials leading coefficient Legendre polynomials limit point maximal parameter sequence Meixner polynomials monic OPS non-decreasing obtain OPS with respect orthogonal polynomials orthogonality relation orthonormal polynomial P₁(x P˛(x Pn(x Po(x Pollaczek polynomial of degree polynomial sequence positive-definite positive-definite moment functional positive-definite OPS Proof Prove quasi-definite real numbers recurrence formula satisfy Show spectrum Stieltjes-Wigert polynomials symmetric Szegö Tchebichef polynomials Theorem 3.2 theory true interval weight function zeros of P(x λη+1