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1: René F. Swarttouw
Swarttouw is mainly a teacher of mathematics and has published a few papers on special functions and orthogonal polynomials. He is coauthor of the book Hypergeometric Orthogonal Polynomials and Their q -AnaloguesHypergeometric Orthogonal Polynomials and Their q -Analogues. …
  • 2: 18.37 Classical OP’s in Two or More Variables
    Orthogonality
    The following three conditions, taken together, determine R m , n ( α ) ( z ) uniquely: …
    §18.37(ii) OP’s on the Triangle
    Orthogonality
    Orthogonal polynomials associated with root systems are certain systems of trigonometric polynomials in several variables, symmetric under a certain finite group (Weyl group), and orthogonal on a torus. …
    3: 18.36 Miscellaneous Polynomials
    Sobolev OP’s are orthogonal with respect to an inner product involving derivatives. …
    §18.36(iii) Multiple OP’s
    These are polynomials in one variable that are orthogonal with respect to a number of different measures. …
    §18.36(iv) Orthogonal Matrix Polynomials
    These are matrix-valued polynomials that are orthogonal with respect to a square matrix of measures on the real line. …
    4: 16.7 Relations to Other Functions
    §16.7 Relations to Other Functions
    For orthogonal polynomials see Chapter 18. …
    5: 18.40 Methods of Computation
    Orthogonal polynomials can be computed from their explicit polynomial form by Horner’s scheme (§1.11(i)). … 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. …
    6: Roelof Koekoek
    Koekoek is mainly a teacher of mathematics and has published a few papers on orthogonal polynomials. He is also author of the book Hypergeometric Orthogonal Polynomials and Their q -Analogues (with P. …
  • 7: 18.38 Mathematical Applications
    Quadrature
    Integrable Systems
    Riemann–Hilbert Problems
    Radon Transform
    Group Representations
    8: 18 Orthogonal Polynomials
    Chapter 18 Orthogonal Polynomials
    9: 32.15 Orthogonal Polynomials
    §32.15 Orthogonal Polynomials
    10: 18.39 Physical Applications
    §18.39 Physical Applications
    §18.39(i) Quantum Mechanics
    The corresponding eigenfunctions are … For physical applications of q -Laguerre polynomials see §17.17. …