DLMF:34.5.E11 (Q10443)

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DLMF:34.5.E11
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    Statements

    DLMF defining formula
    ( 2 ⁢ j 1 + 1 ) ⁢ ( ( J 3 + J 2 - J 1 ) ⁢ ( L 3 + L 2 - J 1 ) - 2 ⁢ ( J 3 ⁢ L 3 + J 2 ⁢ L 2 - J 1 ⁢ L 1 ) ) ⁢ 6 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ l 1 ⁢ l 2 ⁢ l 3 = j 1 ⁢ E ⁢ ( j 1 + 1 ) ⁢ 6 ⁢ j ⁢ j 1 + 1 ⁢ j 2 ⁢ j 3 ⁢ l 1 ⁢ l 2 ⁢ l 3 + ( j 1 + 1 ) ⁢ E ⁢ ( j 1 ) ⁢ 6 ⁢ j ⁢ j 1 - 1 ⁢ j 2 ⁢ j 3 ⁢ l 1 ⁢ l 2 ⁢ l 3 , 2 subscript 𝑗 1 1 subscript 𝐽 3 subscript 𝐽 2 subscript 𝐽 1 subscript 𝐿 3 subscript 𝐿 2 subscript 𝐽 1 2 subscript 𝐽 3 subscript 𝐿 3 subscript 𝐽 2 subscript 𝐿 2 subscript 𝐽 1 subscript 𝐿 1 sixj subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑙 1 subscript 𝑙 2 subscript 𝑙 3 subscript 𝑗 1 𝐸 subscript 𝑗 1 1 sixj subscript 𝑗 1 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑙 1 subscript 𝑙 2 subscript 𝑙 3 subscript 𝑗 1 1 𝐸 subscript 𝑗 1 sixj subscript 𝑗 1 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑙 1 subscript 𝑙 2 subscript 𝑙 3 {\displaystyle{\displaystyle{(2j_{1}+1)\left((J_{3}+J_{2}-J_{1})(L_{3}+L_{2}-J% _{1})-2(J_{3}L_{3}+J_{2}L_{2}-J_{1}L_{1})\right)\mathit{6j}{j_{1}}{j_{2}}{j_{3% }}{l_{1}}{l_{2}}{l_{3}}}\\ =j_{1}E(j_{1}+1)\mathit{6j}{j_{1}+1}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}+(j_{1}% +1)E(j_{1})\mathit{6j}{j_{1}-1}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}},}}
    0 references
    Symbols used
    $$\mathit{6j}$$ symbol
    DLMF defining formula
    6 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ l 1 ⁢ l sixj subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑙 1 𝑙 {\displaystyle{\displaystyle\mathit{6j}{\NVar{j_{1}}}{\NVar{j_{2}}}{\NVar{j_{3% }}}{\NVar{l_{1}}}{\NVar{l}\)\@add@PDF@RDFa@triples\end{document}}}}
    xml-id
    C34.S4.E1.m2ajdec
    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.m1jdec
    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.m1cdec
    0 references
    J r
    DLMF defining formula
    J r subscript 𝐽 𝑟 {\displaystyle{\displaystyle J_{r}}}
    xml-id
    C34.S5.XMD1.m1dec
    0 references

    Identifiers

     
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