Digital Library of Mathematical Functions
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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

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

see Condon and Shortley (1935). For other notations see Edmonds (1974, pp. 52, 97, 104–105) and Varshalovich et al. (1988, §§8.11, 9.10, 10.10).