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DLMF:34.4.E1 - MaRDI portal

DLMF:34.4.E1 (Q10430)

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DLMF:34.4.E1
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    Statements

    DLMF defining formula
    6 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ l 1 ⁢ l 2 ⁢ l 3 = ∑ m r ⁢ m s ′ ( - 1 ) l 1 + m 1 ′ + l 2 + m 2 ′ + l 3 + m 3 ′ ⁢ 3 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ m 1 ⁢ m 2 ⁢ m 3 ⁢ 3 ⁢ j ⁢ j 1 ⁢ l 2 ⁢ l 3 ⁢ m 1 ⁢ m 2 ′ - m 3 ′ ⁢ 3 ⁢ j ⁢ l 1 ⁢ j 2 ⁢ l 3 - m 1 ′ ⁢ m 2 ⁢ m 3 ′ ⁢ 3 ⁢ j ⁢ l 1 ⁢ l 2 ⁢ j 3 ⁢ m 1 ′ - m 2 ′ ⁢ m 3 , sixj subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑙 1 subscript 𝑙 2 subscript 𝑙 3 subscript subscript 𝑚 𝑟 subscript superscript 𝑚 ′ 𝑠 superscript 1 subscript 𝑙 1 subscript superscript 𝑚 ′ 1 subscript 𝑙 2 subscript superscript 𝑚 ′ 2 subscript 𝑙 3 subscript superscript 𝑚 ′ 3 threej subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑚 1 subscript 𝑚 2 subscript 𝑚 3 threej subscript 𝑗 1 subscript 𝑙 2 subscript 𝑙 3 subscript 𝑚 1 subscript superscript 𝑚 ′ 2 subscript superscript 𝑚 ′ 3 threej subscript 𝑙 1 subscript 𝑗 2 subscript 𝑙 3 subscript superscript 𝑚 ′ 1 subscript 𝑚 2 subscript superscript 𝑚 ′ 3 threej subscript 𝑙 1 subscript 𝑙 2 subscript 𝑗 3 subscript superscript 𝑚 ′ 1 subscript superscript 𝑚 ′ 2 subscript 𝑚 3 {\displaystyle{\displaystyle\mathit{6j}{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{% 3}}=\sum_{m_{r}m^{\prime}_{s}}(-1)^{l_{1}+m^{\prime}_{1}+l_{2}+m^{\prime}_{2}+% l_{3}+m^{\prime}_{3}}\*\mathit{3j}{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}}% \mathit{3j}{j_{1}}{l_{2}}{l_{3}}{m_{1}}{m^{\prime}_{2}}{-m^{\prime}_{3}}% \mathit{3j}{l_{1}}{j_{2}}{l_{3}}{-m^{\prime}_{1}}{m_{2}}{m^{\prime}_{3}}% \mathit{3j}{l_{1}}{l_{2}}{j_{3}}{m^{\prime}_{1}}{-m^{\prime}_{2}}{m_{3}},}}
    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
    non-negative integers or non-negative integers plus one half.
    DLMF defining formula
    l , l r 𝑙 subscript 𝑙 𝑟 {\displaystyle{\displaystyle l,l_{r}}}
    xml-id
    C34.S1.XMD2.m1dec
    0 references
    nonnegative integer
    DLMF defining formula
    r 𝑟 {\displaystyle{\displaystyle r}}
    xml-id
    C34.S1.XMD3.m1dec
    0 references

    Identifiers

     
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