classical orthogonal polynomials
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1: 18.38 Mathematical Applications
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§18.38(i) Classical OP’s: Numerical Analysis
… ►Quadrature
… ►Integrable Systems
… ►Riemann–Hilbert Problems
… ►Radon Transform
…2: 18.39 Physical Applications
§18.39 Physical Applications
►§18.39(i) Quantum Mechanics
… ►The corresponding eigenfunctions are … ► … ►For physical applications of -Laguerre polynomials see §17.17. …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: 18.41 Tables
5: 18.13 Continued Fractions
6: 18.3 Definitions
§18.3 Definitions
… ►Name | Constraints | ||||||
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7: 18.5 Explicit Representations
§18.5 Explicit Representations
… ► … ►§18.5(iii) Finite Power Series, the Hypergeometric Function, and Generalized Hypergeometric Functions
… ► … ►8: 18.18 Sums
§18.18 Sums
… ►§18.18(ii) Addition Theorems
… ►§18.18(iii) Multiplication Theorems
… ►§18.18(iv) Connection Formulas
… ►9: 18.14 Inequalities
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