Verblunsky coefficients
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11—20 of 241 matching pages
11: 28.19 Expansions in Series of Functions
12: 26.16 Multiset Permutations
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►The number of elements in is the multinomial coefficient (§26.4) .
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►Thus , and
►The
-multinomial coefficient is defined in terms of Gaussian polynomials (§26.9(ii)) by
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26.16.1
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26.16.2
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13: 33.8 Continued Fractions
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33.8.2
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14: 24.6 Explicit Formulas
15: 20.6 Power Series
16: 2.9 Difference Equations
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►Often and can be expanded in series
…Formal solutions are
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, and higher coefficients are determined by formal substitution.
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►with and higher coefficients given by (2.9.7) (in the present case the coefficients of and are zero).
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►The coefficients
and constant are again determined by formal substitution, beginning with when , or with when .
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17: Errata
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►In regard to orthogonal polynomials on the unit circle, we now discuss monic polynomials, Verblunsky’s Theorem, and Szegő’s theorem.
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Section 16.11(i)
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Additions
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Section 34.1
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Equation (10.20.14)
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10.20.14
Originally this coefficient was given incorrectly as . The other coefficients in this equation have not been changed.
Reported 2012-05-11 by Antony Lee.
18: 16.24 Physical Applications
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§16.24(iii) , , and Symbols
►The symbols, or Clebsch–Gordan coefficients, play an important role in the decomposition of reducible representations of the rotation group into irreducible representations. …The coefficients of transformations between different coupling schemes of three angular momenta are related to the Wigner symbols. …19: 33.20 Expansions for Small
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►where
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33.20.4
,
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►The functions and are as in §§10.2(ii), 10.25(ii), and the coefficients
are given by , , and
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►where is given by (33.14.11), (33.14.12), and
…The functions and are as in §§10.2(ii), 10.25(ii), and the coefficients
are given by (33.20.6).
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