►For exact values of the coefficients of the Jacobipolynomials
, the ultraspherical polynomials
, the Chebyshev polynomials
and , the Legendre polynomials
, the Laguerre polynomials
, and the Hermite polynomials
, see Abramowitz and Stegun (1964, pp. 793–801).
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►However, most of these formulas can be obtained by specialization of formulas for Jacobipolynomials, via (18.7.4)–(18.7.6).
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►►►Figure 18.4.1: Jacobipolynomials
, .
Magnify►►►Figure 18.4.2: Jacobipolynomials
, .
This illustrates inequalities for extrema of a Jacobipolynomial; see (18.14.16).
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Magnify
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