Levi-Civita symbol
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11: 34.9 Graphical Method
§34.9 Graphical Method
►The graphical method establishes a one-to-one correspondence between an analytic expression and a diagram by assigning a graphical symbol to each function and operation of the analytic expression. …For specific examples of the graphical method of representing sums involving the , and symbols, see Varshalovich et al. (1988, Chapters 11, 12) and Lehman and O’Connell (1973, §3.3).12: 34.1 Special Notation
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►The main functions treated in this chapter are the Wigner
symbols, respectively,
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►An often used alternative to the
symbol is the Clebsch–Gordan coefficient
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nonnegative integers. | |
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34.1.1
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►For other notations for , ,
symbols, see Edmonds (1974, pp. 52, 97, 104–105) and Varshalovich et al. (1988, §§8.11, 9.10, 10.10).
13: 34 3j, 6j, 9j Symbols
Chapter 34 Symbols
…14: 34.8 Approximations for Large Parameters
§34.8 Approximations for Large Parameters
►For large values of the parameters in the , , and symbols, different asymptotic forms are obtained depending on which parameters are large. … ►and the symbol denotes a quantity that tends to zero as the parameters tend to infinity, as in §2.1(i). … ►Uniform approximations in terms of Airy functions for the and symbols are given in Schulten and Gordon (1975b). For approximations for the , , and symbols with error bounds see Flude (1998), Chen et al. (1999), and Watson (1999): these references also cite earlier work.15: Peter Paule
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► 1958 in Ried im Innkreis, Austria) is Professor of Mathematics (successor to Bruno Buchberger), Director of the Research Institute for Symbolic Computation (RISC), and Director of the Doctoral Program on Computational Mathematics at the Johannes Kepler University, Linz, Austria.
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►He is on the editorial boards for the Journal of Symbolic Computation and The Ramanujan Journal, and is Managing Editor of Annals of Combinatorics.
He is also Editor-in-Chief of the Springer book series Texts and Monographs in
Symbolic Computation.
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16: 15.11 Riemann’s Differential Equation
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►The complete set of solutions of (15.11.1) is denoted by Riemann’s -symbol:
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15.11.3
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15.11.4
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►Symbolically:
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15.11.6
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17: 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. …Lastly, special cases of the symbols are functions with unit argument. …18: 34.7 Basic Properties: Symbol
§34.7 Basic Properties: Symbol
… ►§34.7(ii) Symmetry
… ►§34.7(iv) Orthogonality
… ►§34.7(vi) Sums
… ►It constitutes an addition theorem for the symbol. …19: 27.1 Special Notation
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positive integers (unless otherwise indicated). | |
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Jacobi symbol; see §27.9. | |
Legendre symbol; see §27.9. |