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DLMF:34.5.E16 - MaRDI portal

DLMF:34.5.E16 (Q10449)

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DLMF:34.5.E16
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    Statements

    DLMF defining formula
    ( - 1 ) j 1 + j 2 + j 3 + j 1 ′ + j 2 ′ + l 1 + l 2 ⁢ 6 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ l 1 ⁢ l 2 ⁢ l 3 ⁢ 6 ⁢ j ⁢ j 1 ′ ⁢ j 2 ′ ⁢ j 3 ⁢ l 1 ⁢ l 2 ⁢ l 3 ′ = ∑ j ( - 1 ) l 3 + l 3 ′ + j ⁢ ( 2 ⁢ j + 1 ) ⁢ 6 ⁢ j ⁢ j 1 ⁢ j 1 ′ ⁢ j ⁢ j 2 ′ ⁢ j 2 ⁢ j 3 ⁢ 6 ⁢ j ⁢ l 3 ⁢ l 3 ′ ⁢ j ⁢ j 1 ′ ⁢ j 1 ⁢ l 2 ⁢ 6 ⁢ j ⁢ l 3 ⁢ l 3 ′ ⁢ j ⁢ j 2 ′ ⁢ j 2 ⁢ l 1 . superscript 1 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 superscript subscript 𝑗 1 ′ superscript subscript 𝑗 2 ′ subscript 𝑙 1 subscript 𝑙 2 sixj subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑙 1 subscript 𝑙 2 subscript 𝑙 3 sixj superscript subscript 𝑗 1 ′ superscript subscript 𝑗 2 ′ subscript 𝑗 3 subscript 𝑙 1 subscript 𝑙 2 superscript subscript 𝑙 3 ′ subscript 𝑗 superscript 1 subscript 𝑙 3 superscript subscript 𝑙 3 ′ 𝑗 2 𝑗 1 sixj subscript 𝑗 1 superscript subscript 𝑗 1 ′ 𝑗 superscript subscript 𝑗 2 ′ subscript 𝑗 2 subscript 𝑗 3 sixj subscript 𝑙 3 superscript subscript 𝑙 3 ′ 𝑗 superscript subscript 𝑗 1 ′ subscript 𝑗 1 subscript 𝑙 2 sixj subscript 𝑙 3 superscript subscript 𝑙 3 ′ 𝑗 superscript subscript 𝑗 2 ′ subscript 𝑗 2 subscript 𝑙 1 {\displaystyle{\displaystyle(-1)^{j_{1}+j_{2}+j_{3}+j_{1}^{\prime}+j_{2}^{% \prime}+l_{1}+l_{2}}\mathit{6j}{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{3}}% \mathit{6j}{j_{1}^{\prime}}{j_{2}^{\prime}}{j_{3}}{l_{1}}{l_{2}}{l_{3}^{\prime% }}=\sum_{j}(-1)^{l_{3}+l_{3}^{\prime}+j}(2j+1)\mathit{6j}{j_{1}}{j_{1}^{\prime% }}{j}{j_{2}^{\prime}}{j_{2}}{j_{3}}\mathit{6j}{l_{3}}{l_{3}^{\prime}}{j}{j_{1}% ^{\prime}}{j_{1}}{l_{2}}\mathit{6j}{l_{3}}{l_{3}^{\prime}}{j}{j_{2}^{\prime}}{% j_{2}}{l_{1}}.}}
    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.m2amdec
    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.m1odec
    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.m1gdec
    0 references

    Identifiers

     
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