DLMF:1.3.E15 (Q44)

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DLMF:1.3.E15
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    Statements

    DLMF defining formula
    | a 1 a 2 ⋯ a n a n a 1 ⋯ a n - 1 ⋮ ⋮ ⋱ ⋮ a 2 a 3 ⋯ a 1 | = ∏ k = 1 n ( a 1 + a 2 ⁢ ω k + a 3 ⁢ ω k 2 + … + a n ⁢ ω k n - 1 ) , subscript 𝑎 1 subscript 𝑎 2 ⋯ subscript 𝑎 𝑛 subscript 𝑎 𝑛 subscript 𝑎 1 ⋯ subscript 𝑎 𝑛 1 ⋮ ⋮ ⋱ ⋮ subscript 𝑎 2 subscript 𝑎 3 ⋯ subscript 𝑎 1 subscript superscript product 𝑛 𝑘 1 subscript 𝑎 1 subscript 𝑎 2 subscript 𝜔 𝑘 subscript 𝑎 3 superscript subscript 𝜔 𝑘 2 … subscript 𝑎 𝑛 superscript subscript 𝜔 𝑘 𝑛 1 {\displaystyle{\displaystyle\begin{vmatrix}a_{1}&a_{2}&\cdots&a_{n}\\ a_{n}&a_{1}&\cdots&a_{n-1}\\ \vdots&\vdots&\ddots&\vdots\\ a_{2}&a_{3}&\cdots&a_{1}\end{vmatrix}=\prod^{n}_{k=1}(a_{1}+a_{2}\omega_{k}+a_% {3}\omega_{k}^{2}+\dots+a_{n}\omega_{k}^{n-1}),}}
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    comment
    Warning: Falling back to standard tex;
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    Symbols used
    Q10739
    DLMF defining formula
    det {\displaystyle{\displaystyle\det}}
    xml-id
    C1.S3.SS1.m1aldec
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    integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1mdec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1gdec
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    roots of unity
    DLMF defining formula
    ω j subscript 𝜔 𝑗 {\displaystyle{\displaystyle\omega_{j}}}
    xml-id
    C1.S3.XMD4.m1dec
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    Identifiers

     
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