About the Project



(0.001 seconds)

1—10 of 136 matching pages

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
    The following three conditions, taken together, determine R m , n ( α ) ( z ) uniquely: …
    §18.37(ii) OP’s on the Triangle
    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 Orthogonal Polynomials
    Chapter 18 Orthogonal Polynomials
    4: 16.7 Relations to Other Functions
    §16.7 Relations to Other Functions
    For orthogonal polynomials see Chapter 18. …
    5: 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. …
  • 6: 32.15 Orthogonal Polynomials
    §32.15 Orthogonal Polynomials
    7: Wolter Groenevelt
    Groenevelt’s research interests is in special functions and orthogonal polynomials and their relations with representation theory and interacting particle systems. As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials. …
    8: 12.16 Mathematical Applications
    For examples see §§13.20(iii), 13.20(iv), 14.15(v), and 14.26. Sleeman (1968b) considers certain orthogonality properties of the PCFs and corresponding eigenvalues. …
    9: 18.21 Hahn Class: Interrelations
    §18.21 Hahn Class: Interrelations
    §18.21(i) Dualities
    §18.21(ii) Limit Relations and Special Cases
    Hahn Jacobi
    Meixner Laguerre
    10: 18.3 Definitions
    §18.3 Definitions
  • 3.

    As given by a Rodrigues formula (18.5.5).

  • Table 18.3.1 provides the traditional definitions of Jacobi, Laguerre, and Hermite polynomials via orthogonality and standardization (§§18.2(i) and 18.2(iii)). … For another version of the discrete orthogonality property of the polynomials T n ( x ) see (3.11.9). … However, in general they are not orthogonal with respect to a positive measure, but a finite system has such an orthogonality. …