DLMF:34.3.E5 (Q9720)

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DLMF:34.3.E5
No description defined

    Statements

    Defining formula
    3 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ 000 = { 0 , J  odd , ( - 1 ) 1 2 ⁢ J ⁢ ( ( J - 2 ⁢ j 1 ) ! ⁢ ( J - 2 ⁢ j 2 ) ! ⁢ ( J - 2 ⁢ j 3 ) ! ( J + 1 ) ! ) 1 2 ⁢ ( 1 2 ⁢ J ) ! ( 1 2 ⁢ J - j 1 ) ! ⁢ ( 1 2 ⁢ J - j 2 ) ! ⁢ ( 1 2 ⁢ J - j 3 ) ! , J  even . threej subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 000 cases 0 J  odd superscript 1 1 2 𝐽 superscript 𝐽 2 subscript 𝑗 1 𝐽 2 subscript 𝑗 2 𝐽 2 subscript 𝑗 3 𝐽 1 1 2 1 2 𝐽 1 2 𝐽 subscript 𝑗 1 1 2 𝐽 subscript 𝑗 2 1 2 𝐽 subscript 𝑗 3 J  even {\displaystyle{\displaystyle\mathit{3j}{j_{1}}{j_{2}}{j_{3}}{0}{0}{0}=\begin{% cases}0,&\mbox{$J$ odd},\\ (-1)^{\frac{1}{2}J}\left(\dfrac{(J-2j_{1})!(J-2j_{2})!(J-2j_{3})!}{(J+1)!}% \right)^{\frac{1}{2}}\dfrac{(\frac{1}{2}J)!}{(\frac{1}{2}J-j_{1})!(\frac{1}{2}% J-j_{2})!(\frac{1}{2}J-j_{3})!},&\mbox{$J$ even}.\end{cases}}}
    0 references
    DLMF id
    DLMF:34.3.E5
    0 references
    Symbols used
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
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    $$\mathit{3j}$$ symbol
    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.m2acdec
    0 references
    Q12709
    Defining formula
    j , j r 𝑗 subscript 𝑗 𝑟 {\displaystyle{\displaystyle j,j_{r}}}
    xml-id
    C34.S1.XMD1.m1ddec
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    sum (locally)
    Defining formula
    J 𝐽 {\displaystyle{\displaystyle J}}
    xml-id
    C34.S3.XMD1.m1adec
    0 references
     
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