general orthogonal polynomials
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1: 18.2 General Orthogonal Polynomials
§18.2 General Orthogonal Polynomials
… ►Orthogonality on Intervals
… ►§18.2(ii) -Difference Operators
… ► … ►§18.2(v) Christoffel–Darboux Formula
…2: Bibliography I
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An electrostatics model for zeros of general orthogonal polynomials.
Pacific J. Math. 193 (2), pp. 355–369.
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3: 18.40 Methods of Computation
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►However, for applications in which the OP’s appear only as terms in series expansions (compare §18.18(i)) the need to compute them can be avoided altogether by use instead of Clenshaw’s algorithm (§3.11(ii)) and its straightforward generalization to OP’s other than Chebyshev.
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4: Richard A. Askey
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►One of his most influential papers Some basic hypergeometric orthogonal polynomials that generalize Jacobi polynomials (with J.
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5: 18.30 Associated OP’s
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Associated Jacobi Polynomials
…6: Howard S. Cohl
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►Cohl has published papers in orthogonal polynomials and special functions, and is particularly interested in fundamental solutions of linear partial differential equations on Riemannian manifolds, associated Legendre functions, generalized and basic hypergeometric functions, eigenfunction expansions of fundamental solutions in separable coordinate systems for linear partial differential equations, orthogonal polynomial generating function and generalized expansions, and -series.
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7: 16.7 Relations to Other Functions
§16.7 Relations to Other Functions
…8: 18.5 Explicit Representations
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§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions
…9: 18.26 Wilson Class: Continued
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§18.26(i) Representations as Generalized Hypergeometric Functions
… ►§18.26(iv) Generating Functions
…10: Bibliography B
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Padé-type Approximation and General Orthogonal Polynomials.
International Series of Numerical Mathematics, Vol. 50, Birkhäuser Verlag, Basel.
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