DLMF:1.6.E14 (Q193)

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DLMF:1.6.E14
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    Statements

    test
    ϵ j ⁣ k ⁣ ℓ = { + 1 , if  ⁢ j , k , ℓ ⁢  is even permutation of  ⁢ 1 , 2 , 3 , - 1 , if  ⁢ j , k , ℓ ⁢  is odd permutation of  ⁢ 1 , 2 , 3 , 0 , otherwise . Levi-Civita 𝑗 𝑘 ℓ cases 1 if  𝑗 𝑘 ℓ  is even permutation of  1 2 3 1 if  𝑗 𝑘 ℓ  is odd permutation of  1 2 3 0 otherwise {\displaystyle{\displaystyle\epsilon_{jk\ell}=\begin{cases}+1,&\text{if }j,k,% \ell\text{ is even permutation of }1,2,3,\\ -1,&\text{if }j,k,\ell\text{ is odd permutation of }1,2,3,\\ \phantom{-}0,&\text{otherwise}.\end{cases}}}
    0 references
    DLMF id
    DLMF:1.6.E14
    0 references
    Symbols used
    Q10763
    test
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C1.S1.XMD3.m1bdec
    0 references
    Q10756
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1dec
    0 references
     
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