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DLMF:34.6.E1 - MaRDI portal

DLMF:34.6.E1 (Q10457)

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DLMF:34.6.E1
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    Statements

    DLMF defining formula
    9 ⁢ j ⁢ j 11 ⁢ j 12 ⁢ j 13 ⁢ j 21 ⁢ j 22 ⁢ j 23 ⁢ j 31 ⁢ j 32 ⁢ j 33 = ∑ all  ⁢ m r ⁢ s 3 ⁢ j ⁢ j 11 ⁢ j 12 ⁢ j 13 ⁢ m 11 ⁢ m 12 ⁢ m 13 ⁢ 3 ⁢ j ⁢ j 21 ⁢ j 22 ⁢ j 23 ⁢ m 21 ⁢ m 22 ⁢ m 23 ⁢ 3 ⁢ j ⁢ j 31 ⁢ j 32 ⁢ j 33 ⁢ m 31 ⁢ m 32 ⁢ m 33 ⁢ 3 ⁢ j ⁢ j 11 ⁢ j 21 ⁢ j 31 ⁢ m 11 ⁢ m 21 ⁢ m 31 ⁢ 3 ⁢ j ⁢ j 12 ⁢ j 22 ⁢ j 32 ⁢ m 12 ⁢ m 22 ⁢ m 32 ⁢ 3 ⁢ j ⁢ j 13 ⁢ j 23 ⁢ j 33 ⁢ m 13 ⁢ m 23 ⁢ m 33 , ninej subscript 𝑗 11 subscript 𝑗 12 subscript 𝑗 13 subscript 𝑗 21 subscript 𝑗 22 subscript 𝑗 23 subscript 𝑗 31 subscript 𝑗 32 subscript 𝑗 33 subscript all  subscript 𝑚 𝑟 𝑠 threej subscript 𝑗 11 subscript 𝑗 12 subscript 𝑗 13 subscript 𝑚 11 subscript 𝑚 12 subscript 𝑚 13 threej subscript 𝑗 21 subscript 𝑗 22 subscript 𝑗 23 subscript 𝑚 21 subscript 𝑚 22 subscript 𝑚 23 threej subscript 𝑗 31 subscript 𝑗 32 subscript 𝑗 33 subscript 𝑚 31 subscript 𝑚 32 subscript 𝑚 33 threej subscript 𝑗 11 subscript 𝑗 21 subscript 𝑗 31 subscript 𝑚 11 subscript 𝑚 21 subscript 𝑚 31 threej subscript 𝑗 12 subscript 𝑗 22 subscript 𝑗 32 subscript 𝑚 12 subscript 𝑚 22 subscript 𝑚 32 threej subscript 𝑗 13 subscript 𝑗 23 subscript 𝑗 33 subscript 𝑚 13 subscript 𝑚 23 subscript 𝑚 33 {\displaystyle{\displaystyle\mathit{9j}{j_{11}}{j_{12}}{j_{13}}{j_{21}}{j_{22}% }{j_{23}}{j_{31}}{j_{32}}{j_{33}}=\sum_{\mbox{\scriptsize all }m_{rs}}\mathit{% 3j}{j_{11}}{j_{12}}{j_{13}}{m_{11}}{m_{12}}{m_{13}}\mathit{3j}{j_{21}}{j_{22}}% {j_{23}}{m_{21}}{m_{22}}{m_{23}}\mathit{3j}{j_{31}}{j_{32}}{j_{33}}{m_{31}}{m_% {32}}{m_{33}}\*\mathit{3j}{j_{11}}{j_{21}}{j_{31}}{m_{11}}{m_{21}}{m_{31}}% \mathit{3j}{j_{12}}{j_{22}}{j_{32}}{m_{12}}{m_{22}}{m_{32}}\mathit{3j}{j_{13}}% {j_{23}}{j_{33}}{m_{13}}{m_{23}}{m_{33}},}}
    0 references
    Symbols used
    $$\mathit{3j}$$ symbol
    DLMF defining formula
    3 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ m 1 ⁢ missing threej subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑚 1 missing {\displaystyle{\displaystyle\mathit{3j}{\NVar{j_{1}}}{\NVar{j_{2}}}{\NVar{j_{3% }}}{\NVar{m_{1}}}{\NVar{missing}\)\@add@PDF@RDFa@triples\end{document}}}}
    xml-id
    C34.S2.E4.m2adec
    0 references
    non-negative integers or non-negative integers plus one half.
    DLMF defining formula
    j , j r 𝑗 subscript 𝑗 𝑟 {\displaystyle{\displaystyle j,j_{r}}}
    xml-id
    C34.S1.XMD1.m1dec
    0 references
    nonnegative integer
    DLMF defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C34.S1.XMD3.m1dec
    0 references
    integer
    DLMF defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C34.S6.XMD1.m1dec
    0 references

    Identifiers

     
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