DLMF:34.3.E6 (Q9721): Difference between revisions

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Revision as of 14:41, 2 January 2020

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DLMF:34.3.E6
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    3 j j 1 j 2 j 1 + j 2 m 1 m 2 - m 1 - m 2 = ( - 1 ) j 1 - j 2 + m 1 + m 2 ( ( 2 j 1 ) ! ( 2 j 2 ) ! ( j 1 + j 2 + m 1 + m 2 ) ! ( j 1 + j 2 - m 1 - m 2 ) ! ( 2 j 1 + 2 j 2 + 1 ) ! ( j 1 + m 1 ) ! ( j 1 - m 1 ) ! ( j 2 + m 2 ) ! ( j 2 - m 2 ) ! ) 1 2 , threej subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑚 1 subscript 𝑚 2 subscript 𝑚 1 subscript 𝑚 2 superscript 1 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑚 1 subscript 𝑚 2 superscript 2 subscript 𝑗 1 2 subscript 𝑗 2 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑚 1 subscript 𝑚 2 subscript 𝑗 1 subscript 𝑗 2 subscript 𝑚 1 subscript 𝑚 2 2 subscript 𝑗 1 2 subscript 𝑗 2 1 subscript 𝑗 1 subscript 𝑚 1 subscript 𝑗 1 subscript 𝑚 1 subscript 𝑗 2 subscript 𝑚 2 subscript 𝑗 2 subscript 𝑚 2 1 2 {\displaystyle{\displaystyle\mathit{3j}{j_{1}}{j_{2}}{j_{1}+j_{2}}{m_{1}}{m_{2% }}{-m_{1}-m_{2}}=(-1)^{j_{1}-j_{2}+m_{1}+m_{2}}\left(\frac{(2j_{1})!(2j_{2})!(% j_{1}+j_{2}+m_{1}+m_{2})!(j_{1}+j_{2}-m_{1}-m_{2})!}{(2j_{1}+2j_{2}+1)!(j_{1}+% m_{1})!(j_{1}-m_{1})!(j_{2}+m_{2})!(j_{2}-m_{2})!}\right)^{\frac{1}{2}},}}
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    DLMF:34.3.E6
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    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5aadec
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