SO（n）的对称表示为二重级数的6 j-符号
6j-symbols for symmetric representations of SO(n) as the double series
摘要：
修正了Ališauskas（1987）关于再耦合（Racah）系数的三重和表达式（6 j-符号）的对称正交群SO（n）的（最退化）表示（以前从Ališauskas的四重和表达式导出，也与Hormeßand Junker 1999的结果有关）被重新排列成三个新的不同的双和表达式（与超几何的Kampé de Fériet型级数有关）和一个新的具有较好求和条件的三重和表达式。揭示了正交群SO（n）的特殊6 j-符号关于特殊Kampé de Fériet $F_{1:3}^{1:4}$级数的Regge型对称性.利用辛群Sp（2n）的反对称表示的再耦合系数与形式正交群SO（-2n）的再耦合系数的关系，导出了它们的再耦合系数.
英文摘要：
The corrected triple sum expression of Ališauskas (1987) for the recoupling (Racah) coefficients (6j-symbols) of the symmetric (most degenerate) representations of the orthogonal groups SO(n) (previously derived from the fourfold sum expression of Ališauskas also related to result of Hormeßand Junker 1999) is rearranged into three new different double sum expressions (related to the hypergeometric Kampé de Fériet type series) and a new triple sum expression with preferable summation condition. The Regge type symmetry of special 6j-symbols of the orthogonal groups SO(n) in terms of special Kampé de Fériet $F_{1:3}^{1:4}$ series is revealed. The recoupling coefficients for antisymmetric representations of symplectic group Sp(2n) are derived using their relation with the recoupling coefficients of the formal orthogonal group SO(-2n).
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