ultraspherical polynomials
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1: 18.3 Definitions
§18.3 Definitions
… ►This table also includes the following special cases of Jacobi polynomials: ultraspherical, Chebyshev, and Legendre. ►Name | Constraints | ||||||
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Ultraspherical (Gegenbauer) | |||||||
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2: 18.6 Symmetry, Special Values, and Limits to Monomials
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►For Jacobi, ultraspherical, Chebyshev, Legendre, and Hermite polynomials, see Table 18.6.1.
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§18.6(ii) Limits to Monomials
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18.6.4
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3: 18.7 Interrelations and Limit Relations
4: 18.9 Recurrence Relations and Derivatives
5: 18.1 Notation
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►In Szegő (1975, §4.7) the ultraspherical polynomials
are denoted by .
The ultraspherical polynomials will not be considered for .
They are defined in the literature by and
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Ultraspherical (or Gegenbauer): .
Continuous -Ultraspherical: .
6: 18.10 Integral Representations
7: 37.4 Disk with Weight Function
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37.4.5
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37.4.6
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►There is also an orthogonal basis of consisting of polynomials
().
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►For , by (18.7.4), , the Chebyshev polynomial of the second kind.
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37.4.29
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