►For expressions of ultraspherical, Chebyshev, and Legendre polynomials in terms of Jacobipolynomials, see §18.7(i).
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►For a finite system of Jacobipolynomials
is orthogonal on with weight function .
For and a finite system of Jacobipolynomials
(called pseudo Jacobipolynomials or Routh–Romanovski polynomials) is orthogonal on with .
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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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