DLMF:34.6.E2 (Q9766): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: $$\mathit{9j}$$ symbol / rank
 
Normal rank
Property / Symbols used: $$\mathit{9j}$$ symbol / qualifier
 
Defining formula:

9 ⁢ j ⁢ j 11 ⁢ j 12 ⁢ j 13 ⁢ j 21 ninej subscript 𝑗 11 subscript 𝑗 12 subscript 𝑗 13 subscript 𝑗 21 {\displaystyle{\displaystyle\mathit{9j}{\NVar{j_{11}}}{\NVar{j_{12}}}{\NVar{j_% {13}}}{\NVar{j_{21}}}{\)\@add@PDF@RDFa@triples\end{document}}}}

\Wignerninejsym{\NVar{j_{11}}}{\NVar{j_{12}}}{\NVar{j_{13}}}{\NVar{j_{21}}}{% \NVar{j_{22}}}{\NVar{j_{23}}}{\NVar{j_{31}}}{\NVar{j_{32}}}{\NVar{j_{33}}}
Property / Symbols used: $$\mathit{9j}$$ symbol / qualifier
 
xml-id: C34.S6.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: $$\mathit{6j}$$ symbol / rank
 
Normal rank
Property / Symbols used: $$\mathit{6j}$$ symbol / qualifier
 
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}}}}

\Wignersixjsym{\NVar{j_{1}}}{\NVar{j_{2}}}{\NVar{j_{3}}}{\NVar{l_{1}}}{\NVar{l% _{2}}}{\NVar{l_{3}}}
Property / Symbols used: $$\mathit{6j}$$ symbol / qualifier
 
xml-id: C34.S4.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12709 / rank
 
Normal rank
Property / Symbols used: Q12709 / qualifier
 
Defining formula:

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.m1adec

Latest revision as of 14:45, 2 January 2020

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DLMF:34.6.E2
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    Statements

    Defining formula
    9 ⁢ j ⁢ j 11 ⁢ j 12 ⁢ j 13 ⁢ j 21 ⁢ j 22 ⁢ j 23 ⁢ j 31 ⁢ j 32 ⁢ j 33 = ∑ j ( - 1 ) 2 ⁢ j ⁢ ( 2 ⁢ j + 1 ) ⁢ 6 ⁢ j ⁢ j 11 ⁢ j 21 ⁢ j 31 ⁢ j 32 ⁢ j 33 ⁢ j ⁢ 6 ⁢ j ⁢ j 12 ⁢ j 22 ⁢ j 32 ⁢ j 21 ⁢ j ⁢ j 23 ⁢ 6 ⁢ j ⁢ j 13 ⁢ j 23 ⁢ j 33 ⁢ j ⁢ j 11 ⁢ j 12 . ninej subscript 𝑗 11 subscript 𝑗 12 subscript 𝑗 13 subscript 𝑗 21 subscript 𝑗 22 subscript 𝑗 23 subscript 𝑗 31 subscript 𝑗 32 subscript 𝑗 33 subscript 𝑗 superscript 1 2 𝑗 2 𝑗 1 sixj subscript 𝑗 11 subscript 𝑗 21 subscript 𝑗 31 subscript 𝑗 32 subscript 𝑗 33 𝑗 sixj subscript 𝑗 12 subscript 𝑗 22 subscript 𝑗 32 subscript 𝑗 21 𝑗 subscript 𝑗 23 sixj subscript 𝑗 13 subscript 𝑗 23 subscript 𝑗 33 𝑗 subscript 𝑗 11 subscript 𝑗 12 {\displaystyle{\displaystyle\mathit{9j}{j_{11}}{j_{12}}{j_{13}}{j_{21}}{j_{22}% }{j_{23}}{j_{31}}{j_{32}}{j_{33}}=\sum_{j}(-1)^{2j}(2j+1)\mathit{6j}{j_{11}}{j% _{21}}{j_{31}}{j_{32}}{j_{33}}{j}\mathit{6j}{j_{12}}{j_{22}}{j_{32}}{j_{21}}{j% }{j_{23}}\mathit{6j}{j_{13}}{j_{23}}{j_{33}}{j}{j_{11}}{j_{12}}.}}
    0 references
    DLMF id
    DLMF:34.6.E2
    0 references
    Symbols used
    $$\mathit{9j}$$ symbol
    Defining formula
    9 ⁢ j ⁢ j 11 ⁢ j 12 ⁢ j 13 ⁢ j 21 ninej subscript 𝑗 11 subscript 𝑗 12 subscript 𝑗 13 subscript 𝑗 21 {\displaystyle{\displaystyle\mathit{9j}{\NVar{j_{11}}}{\NVar{j_{12}}}{\NVar{j_% {13}}}{\NVar{j_{21}}}{\)\@add@PDF@RDFa@triples\end{document}}}}
    xml-id
    C34.S6.E1.m2aadec
    0 references
    $$\mathit{6j}$$ symbol
    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.m2adec
    0 references
    Q12709
    Defining formula
    j , j r 𝑗 subscript 𝑗 𝑟 {\displaystyle{\displaystyle j,j_{r}}}
    xml-id
    C34.S1.XMD1.m1adec
    0 references
     
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