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34 3j, 6j, 9j SymbolsProperties

§34.6 Definition: 9⁒j Symbol

The 9⁒j symbol may be defined either in terms of 3⁒j symbols or equivalently in terms of 6⁒j symbols:

34.6.1 {j11j12j13j21j22j23j31j32j33} =βˆ‘all ⁒mr⁒s(j11j12j13m11m12m13)⁒(j21j22j23m21m22m23)⁒(j31j32j33m31m32m33)Γ—(j11j21j31m11m21m31)⁒(j12j22j32m12m22m32)⁒(j13j23j33m13m23m33),
34.6.2 {j11j12j13j21j22j23j31j32j33} =βˆ‘j(βˆ’1)2⁒j⁒(2⁒j+1)⁒{j11j21j31j32j33j}⁒{j12j22j32j21jj23}⁒{j13j23j33jj11j12}.

The 9⁒j symbol may also be written as a finite triple sum equivalent to a terminating generalized hypergeometric series of three variables with unit arguments. See Srinivasa Rao and Rajeswari (1993, pp. 7 and 125–132) and Rosengren (1999).