relation to 3j symbols
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1: 34.3 Basic Properties: Symbol
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§34.3(vii) Relations to Legendre Polynomials and Spherical Harmonics
… ►Equations (34.3.19)–(34.3.22) are particular cases of more general results that relate rotation matrices to symbols, for which see Edmonds (1974, Chapter 4). …2: 18.38 Mathematical Applications
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3: 16.24 Physical Applications
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§16.24(iii) , , and Symbols
…4: 16.4 Argument Unity
5: 16.7 Relations to Other Functions
6: Bibliography M
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Chebyshev expansions for modified Struve and related functions.
Math. Comp. 60 (202), pp. 735–747.
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Algorithm 757: MISCFUN, a software package to compute uncommon special functions.
ACM Trans. Math. Software 22 (3), pp. 288–301.
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Connection between quantum systems involving the fourth Painlevé transcendent and -step rational extensions of the harmonic oscillator related to Hermite exceptional orthogonal polynomial.
J. Math. Phys. 57 (5), pp. Paper 052101, 15 pp..
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Recursion relations for the -
symbols.
Nuclear Physics A 113 (1), pp. 215–220.
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Evaluation of complex logarithms and related functions.
SIAM J. Numer. Anal. 18 (4), pp. 744–750.
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7: 34.5 Basic Properties: Symbol
§34.5 Basic Properties: Symbol
… ►§34.5(ii) Symmetry
… ►Additional symmetries are obtained by applying (34.5.8) to (34.5.9) and (34.5.10). … ►§34.5(iii) Recursion Relations
… ►§34.5(iv) Orthogonality
…8: 10 Bessel Functions
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9: Bibliography F
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On the reciprocal modulus relation for elliptic integrals.
SIAM J. Math. Anal. 1 (4), pp. 524–526.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. II.
J. Math. Anal. Appl. 7 (3), pp. 440–451.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order.
J. Math. Anal. Appl. 6 (3), pp. 394–403.
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Asymptotic expansions of a class of hypergeometric polynomials with respect to the order. III.
J. Math. Anal. Appl. 12 (3), pp. 593–601.
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The Edmonds asymptotic formulas for the and
symbols.
J. Math. Phys. 39 (7), pp. 3906–3915.
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10: Errata
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Chapters 10 Bessel Functions, 18 Orthogonal Polynomials, 34 3j, 6j, 9j Symbols
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Equations (10.22.37), (10.22.38), (14.17.6)–(14.17.9)
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Section 34.1
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Section 34.1
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Equation (34.3.7)
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The Kronecker delta symbols have been moved furthest to the right, as is common convention for orthogonality relations.
The relation between Clebsch-Gordan and symbols was clarified, and the sign of was changed for readability. The reference Condon and Shortley (1935) for the Clebsch-Gordan coefficients was replaced by Edmonds (1974) and Rotenberg et al. (1959) and the references for , , symbols were made more precise in §34.1.
34.3.7
In the original equation the prefactor of the above 3j symbol read . It is now replaced by its correct value .
Reported 2014-06-12 by James Zibin.