Digital Library of Mathematical Functions
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34 3j,6j,9j SymbolsProperties

§34.10 Zeros

In a 3j symbol, if the three angular momenta j1,j2,j3 do not satisfy the triangle conditions (34.2.1), or if the projective quantum numbers do not satisfy (34.2.3), then the 3j symbol is zero. Similarly the 6j symbol (34.4.1) vanishes when the triangle conditions are not satisfied by any of the four 3j symbols in the summation. Such zeros are called trivial zeros. However, the 3j and 6j symbols may vanish for certain combinations of the angular momenta and projective quantum numbers even when the triangle conditions are fulfilled. Such zeros are called nontrivial zeros.

For further information, including examples of nontrivial zeros and extensions to 9j symbols, see Srinivasa Rao and Rajeswari (1993, pp. 133–215, 294–295, 299–310).