degree lowering and raising

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1: 18.3 Definitions

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With the property that ${\{p_{n+1}^{\prime }(x)\}}_{n=0}^{\mathrm{\infty }}$ is again a system of OP’s. See §18.9(iii).

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2: 18.9 Recurrence Relations and Derivatives

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§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

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Degree lowering and raising differentiation formulas and structure relations

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