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34 3j, 6j, 9j SymbolsNotation

§34.1 Special Notation

(For other notation see Notation for the Special Functions.)

2j1,2j2,2j3,2l1,2l2,2l3 nonnegative integers.
r,s,t nonnegative integers.

The main functions treated in this chapter are the Wigner 3j,6j,9j symbols, respectively,

(j1j2j3m1m2m3),
{j1j2j3l1l2l3},
{j11j12j13j21j22j23j31j32j33}.

The most commonly used alternative notation for the 3j symbol is the Clebsch–Gordan coefficient

34.1.1 (j1m1j2m2|j1j2j3-m3)=(-1)j1-j2-m3(2j3+1)12(j1j2j3m1m2m3);

see Edmonds (1974, p. 46, Eq. (3.7.3)) and Rotenberg et al. (1959, p. 1, Eq. (1.1a)). For other notations for 3j, 6j, 9j symbols, see Edmonds (1974, pp. 52, 97, 104–105) and Varshalovich et al. (1988, §§8.11, 9.10, 10.10).