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degree lowering and raising

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1: 18.3 Definitions
  • 2.

    With the property that { p n + 1 ( x ) } n = 0 is again a system of OP’s. See §18.9(iii).

  • 2: 18.9 Recurrence Relations and Derivatives
    §18.9(iii) Derivatives
    Formula (18.9.15) is degree lowering, while it raises the parameters. Formula (18.9.16) is degree raising, while it lowers the parameters. …
    3: 18.2 General Orthogonal Polynomials
    Degree lowering and raising differentiation formulas and structure relations