About the Project
34 3j, 6j, 9j SymbolsProperties

§34.6 Definition: 9j Symbol

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

34.6.1 {j11j12j13j21j22j23j31j32j33} =all mrs(j11j12j13m11m12m13)(j21j22j23m21m22m23)(j31j32j33m31m32m33)×(j11j21j31m11m21m31)(j12j22j32m12m22m32)(j13j23j33m13m23m33),
34.6.2 {j11j12j13j21j22j23j31j32j33} =j(-1)2j(2j+1){j11j21j31j32j33j}{j12j22j32j21jj23}{j13j23j33jj11j12}.

The 9j 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).