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. |
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According to Theorem Al-Salam Amer An+l Bessel polynomials Carlitz chain sequence Charlier polynomials Chihara class of orthogonal classical orthogonal polynomials continued fraction converges COROLLARY corresponding monic defined definition denote determined differential equation distribution function Erdélyi example finite first follows Gauss quadrature formula Hahn Hamburger moment problem hence Hermite polynomials I-Ex I-Theorem inequality integral interval of orthogonality Jacobi polynomials kernel polynomials Laguerre polynomials leading coefficient Legendre polynomials limit point linear MATHEMATICS maximal parameter sequence Meixner polynomials monic OPS monic polynomials non-decreasing obtain OPS with respect orthogonal polynomials orthogonality relation orthonormal polynomial pn(x Pollaczek polynomial of degree polynomial sequence positive-definite moment functional positive-definite OPS properties Prove Qn(x quasi-definite quasi-orthogonal polynomial real numbers recurrence formula satisfies Show specific spectrum Stieltjes-Wigert polynomials sufficient condition supporting set symmetric Szego Tchebichef polynomials Theorem 3.2 theory true interval verified Wall polynomials weight function write