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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: Bibliography T
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Improved error bounds for the Liouville-Green (or WKB) approximation.
J. Math. Anal. Appl. 85 (1), pp. 79–89.
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The Askey scheme for hypergeometric orthogonal polynomials viewed from asymptotic analysis.
J. Comput. Appl. Math. 133 (1-2), pp. 623–633.
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Angular Momentum: An Illustrated Guide to Rotational Symmetries for Physical Systems.
A Wiley-Interscience Publication, John Wiley & Sons Inc., New York.
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Evaluation of the exponential integral for large complex arguments.
J. Research Nat. Bur. Standards 52, pp. 313–317.
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Six myths of polynomial interpolation and quadrature.
Math. Today (Southend-on-Sea) 47 (4), pp. 184–188.
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14: About the Project
15: 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. …16: 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.17: 34 3j, 6j, 9j Symbols
Chapter 34 Symbols
…18: Bibliography G
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Quasirandom distributed bases for bound problems.
J. Chem. Phys. 114 (9), pp. 3929–3939.
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Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics.
Developments in Mathematics, Vol. 4, Kluwer Academic Publishers, Dordrecht.
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Riemann surfaces, plane algebraic curves and their period matrices.
J. Symbolic Comput. 26 (6), pp. 789–803.
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A new identity for some six-
symbols.
J. Math. Phys. 32 (6), pp. 1430–1432.
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Linear Differential Equations and Group Theory from Riemann to Poincaré.
2nd edition, Birkhäuser Boston Inc., Boston, MA.
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