DLMF:34.3.E14 (Q9729): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: $$\mathit{3j}$$ symbol / rank
 
Normal rank
Property / Symbols used: $$\mathit{3j}$$ symbol / qualifier
 
test:

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}}}}

\Wignerthreejsym{\NVar{j_{1}}}{\NVar{j_{2}}}{\NVar{j_{3}}}{\NVar{m_{1}}}{\NVar% {m_{2}}}{\NVar{m_{3}}}
Property / Symbols used: $$\mathit{3j}$$ symbol / qualifier
 
xml-id: C34.S2.E4.m2aldec
Property / Symbols used
 
Property / Symbols used: Q12709 / rank
 
Normal rank
Property / Symbols used: Q12709 / qualifier
 
test:

j , j r 𝑗 subscript 𝑗 𝑟 {\displaystyle{\displaystyle j,j_{r}}}

j,j_{r}
Property / Symbols used: Q12709 / qualifier
 
xml-id: C34.S1.XMD1.m1mdec

Latest revision as of 13:41, 2 January 2020

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DLMF:34.3.E14
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    Statements

    test
    ( j 1 ⁢ ( j 1 + 1 ) - j 2 ⁢ ( j 2 + 1 ) - j 3 ⁢ ( j 3 + 1 ) - 2 ⁢ m 2 ⁢ m 3 ) ⁢ 3 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ m 1 ⁢ m 2 ⁢ m 3 = ( ( j 2 - m 2 ) ⁢ ( j 2 + m 2 + 1 ) ⁢ ( j 3 - m 3 + 1 ) ⁢ ( j 3 + m 3 ) ) 1 2 ⁢ 3 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ m 1 ⁢ m 2 + 1 ⁢ m 3 - 1 + ( ( j 2 - m 2 + 1 ) ⁢ ( j 2 + m 2 ) ⁢ ( j 3 - m 3 ) ⁢ ( j 3 + m 3 + 1 ) ) 1 2 ⁢ 3 ⁢ j ⁢ j 1 ⁢ j 2 ⁢ j 3 ⁢ m 1 ⁢ m 2 - 1 ⁢ m 3 + 1 , subscript 𝑗 1 subscript 𝑗 1 1 subscript 𝑗 2 subscript 𝑗 2 1 subscript 𝑗 3 subscript 𝑗 3 1 2 subscript 𝑚 2 subscript 𝑚 3 threej subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑚 1 subscript 𝑚 2 subscript 𝑚 3 superscript subscript 𝑗 2 subscript 𝑚 2 subscript 𝑗 2 subscript 𝑚 2 1 subscript 𝑗 3 subscript 𝑚 3 1 subscript 𝑗 3 subscript 𝑚 3 1 2 threej subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑚 1 subscript 𝑚 2 1 subscript 𝑚 3 1 superscript subscript 𝑗 2 subscript 𝑚 2 1 subscript 𝑗 2 subscript 𝑚 2 subscript 𝑗 3 subscript 𝑚 3 subscript 𝑗 3 subscript 𝑚 3 1 1 2 threej subscript 𝑗 1 subscript 𝑗 2 subscript 𝑗 3 subscript 𝑚 1 subscript 𝑚 2 1 subscript 𝑚 3 1 {\displaystyle{\displaystyle\left(j_{1}(j_{1}+1)-j_{2}(j_{2}+1)-j_{3}(j_{3}+1)% -2m_{2}m_{3}\right)\mathit{3j}{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}}{m_{3}}=\left% ((j_{2}-m_{2})(j_{2}+m_{2}+1)(j_{3}-m_{3}+1)(j_{3}+m_{3})\right)^{\frac{1}{2}}% \mathit{3j}{j_{1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}+1}{m_{3}-1}+\left((j_{2}-m_{2}+1% )(j_{2}+m_{2})(j_{3}-m_{3})(j_{3}+m_{3}+1)\right)^{\frac{1}{2}}\mathit{3j}{j_{% 1}}{j_{2}}{j_{3}}{m_{1}}{m_{2}-1}{m_{3}+1},}}
    0 references
    DLMF id
    DLMF:34.3.E14
    0 references
    Symbols used
    $$\mathit{3j}$$ symbol
    test
    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.m2aldec
    0 references
    Q12709
    test
    j , j r 𝑗 subscript 𝑗 𝑟 {\displaystyle{\displaystyle j,j_{r}}}
    xml-id
    C34.S1.XMD1.m1mdec
    0 references
     
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