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• W2110611982 abstract "The expressions for the coupling coefficients (3j-symbols) for most degenerate (symmetric) representations of orthogonal groups SO(n) in a canonical basis (with SO(n) restricted to SO(n − 1) and different semicanonical or tree bases (with SO(n) restricted to SO(n') × SO(n''), n' + n'' = n) are considered, respectively, in context of integrals involving triplets of the Gegenbauer and the Jacobi polynomials. Since the directly derived triple-hypergeometric series do not reveal the apparent triangle conditions of the 3j-symbols, they are rearranged, using their relation with semistretched isofactors of the second kind for the complementary chain Sp(4) ⊃ SU(2) × SU(2) and analogy with the stretched 9j coefficients of SU(2), into formulae with more rich limits for summation intervals and obvious triangle conditions. The isofactors of class-one representations of orthogonal groups or class-two representations of unitary groups (and, of course, the related integrals involving triplets of the Gegenbauer and the Jacobi polynomials) turn into double sums in the cases of canonical SO(n) ⊃ SO(n − 1) or U(n) ⊃ U(n − 1) and semicanonical SO(n) ⊃ SO(n − 2) × SO(2) chains, as well as into the 4F3(1) series under more specific conditions. Some ambiguities of the phase choice of the complementary group approach are adjusted, as well as problems with an alternating sign parameter of SO(2) representations in the SO(3) ⊃ SO(2) and SO(n) ⊃ SO(n − 2) × SO(2) chains." @default.
• W2110611982 created "2016-06-24" @default.
• W2110611982 creator A5027386920 @default.
• W2110611982 date "2002-08-13" @default.
• W2110611982 modified "2023-09-27" @default.
• W2110611982 title "Coupling coefficients of SO(n) and integrals involving Jacobi and Gegenbauer polynomials" @default.
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• W2110611982 doi "https://doi.org/10.1088/0305-4470/35/34/307" @default.
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