Chebyshev polynomials
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1: 18.3 Definitions
§18.3 Definitions
… βΊName | Constraints | ||||||
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Chebyshev of second kind | |||||||
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Shifted Chebyshev of second kind | |||||||
… |
2: 18.41 Tables
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βΊFor () see §14.33.
βΊAbramowitz and Stegun (1964, Tables 22.4, 22.6, 22.11, and 22.13) tabulates , , , and for .
The ranges of are for and , and for and .
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3: 18.9 Recurrence Relations and Derivatives
4: 18.7 Interrelations and Limit Relations
5: 18.5 Explicit Representations
6: 18.1 Notation
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βΊ
βΊ
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βΊNor do we consider the shifted Jacobi polynomials:
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βΊ
βΊ
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Chebyshev of first, second, third, and fourth kinds: , , , .
Shifted Chebyshev of first and second kinds: , .
7: 18.6 Symmetry, Special Values, and Limits to Monomials
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βΊ
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8: 18.13 Continued Fractions
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βΊ
Chebyshev
βΊ is the denominator of the th approximant to: …and is the denominator of the th approximant to: …9: 29.15 Fourier Series and Chebyshev Series
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βΊ
§29.15(ii) Chebyshev Series
βΊThe Chebyshev polynomial of the first kind (§18.3) satisfies . … βΊ
29.15.43
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βΊUsing also , with denoting the Chebyshev polynomial of the second kind (§18.3), we obtain
βΊ
29.15.44
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