q-multinomial coefficient
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11—20 of 241 matching pages
11: 28.19 Expansions in Series of Functions
12: 33.8 Continued Fractions
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33.8.2
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13: 24.6 Explicit Formulas
14: 20.6 Power Series
15: 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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16: 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. …17: 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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18: 18.22 Hahn Class: Recurrence Relations and Differences
19: 34.14 Tables
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►Biedenharn and Louck (1981) give tables of algebraic expressions for Clebsch–Gordan coefficients and symbols, together with a bibliography of tables produced prior to 1975.
In Varshalovich et al. (1988) algebraic expressions for the Clebsch–Gordan coefficients with all parameters and numerical values for all parameters are given on pp.
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