DLMF:34.4.E2 (Q10431)

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DLMF:34.4.E2
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    Statements

    DLMF defining formula
    6 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ l 1 ⁢ l 2 ⁢ l 3 = Δ ⁢ ( j 1 ⁢ j 2 ⁢ j 3 ) ⁢ Δ ⁢ ( j 1 ⁢ l 2 ⁢ l 3 ) ⁢ Δ ⁢ ( l 1 ⁢ j 2 ⁢ l 3 ) ⁢ Δ ⁢ ( l 1 ⁢ l 2 ⁢ j 3 ) ⁢ ∑ s ( - 1 ) s ⁢ ( s + 1 ) ! ( s - j 1 - j 2 - j 3 ) ! ⁢ ( s - j 1 - l 2 - l 3 ) ! ⁢ ( s - l 1 - j 2 - l 3 ) ! ⁢ ( s - l 1 - l 2 - j 3 ) ! ⁢ 1 ( j 1 + j 2 + l 1 + l 2 - s ) ! ⁢ ( j 2 + j 3 + l 2 + l 3 - s ) ! ⁢ ( j 3 + j 1 + l 3 + l 1 - s ) ! , sixj subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑙 1 subscript 𝑙 2 subscript 𝑙 3 Δ subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 Δ subscript 𝑗 1 subscript 𝑙 2 subscript 𝑙 3 Δ subscript 𝑙 1 subscript 𝑗 2 subscript 𝑙 3 Δ subscript 𝑙 1 subscript 𝑙 2 subscript 𝑗 3 subscript 𝑠 superscript 1 𝑠 𝑠 1 𝑠 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 𝑠 subscript 𝑗 1 subscript 𝑙 2 subscript 𝑙 3 𝑠 subscript 𝑙 1 subscript 𝑗 2 subscript 𝑙 3 𝑠 subscript 𝑙 1 subscript 𝑙 2 subscript 𝑗 3 1 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑙 1 subscript 𝑙 2 𝑠 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑙 2 subscript 𝑙 3 𝑠 subscript 𝑗 3 subscript 𝑗 1 subscript 𝑙 3 subscript 𝑙 1 𝑠 {\displaystyle{\displaystyle\mathit{6j}{j_{1}}{j_{2}}{j_{3}}{l_{1}}{l_{2}}{l_{% 3}}=\Delta(j_{1}j_{2}j_{3})\Delta(j_{1}l_{2}l_{3})\Delta(l_{1}j_{2}l_{3})% \Delta(l_{1}l_{2}j_{3})\*\sum_{s}\frac{(-1)^{s}(s+1)!}{(s-j_{1}-j_{2}-j_{3})!(% s-j_{1}-l_{2}-l_{3})!(s-l_{1}-j_{2}-l_{3})!(s-l_{1}-l_{2}-j_{3})!}\*\frac{1}{(% j_{1}+j_{2}+l_{1}+l_{2}-s)!(j_{2}+j_{3}+l_{2}+l_{3}-s)!(j_{3}+j_{1}+l_{3}+l_{1% }-s)!},}}
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    Symbols used
    Q10729
    DLMF defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    $$\mathit{6j}$$ 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.m2abdec
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    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.m1adec
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    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.m1adec
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    product (locally)
    DLMF defining formula
    Δ ⁢ ( j 1 ⁢ j 2 ⁢ j 3 ) Δ subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 {\displaystyle{\displaystyle\Delta(j_{1}j_{2}j_{3})}}
    xml-id
    C34.S2.XMD4.m1dec
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    Identifiers

     
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