DLMF:1.3.E15 (Q75)

From DRMF
Revision as of 15:49, 1 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:1.3.E15
No description defined

    Statements

    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}),}}
    0 references
    DLMF id
    DLMF:1.3.E15
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    Q10765
    Defining formula
    det {\displaystyle{\displaystyle\det}}
    xml-id
    C1.S3.SS1.m1aldec
    0 references
    Q10756
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1mdec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1gdec
    0 references
    Q10767
    Defining formula
    ω j subscript 𝜔 𝑗 {\displaystyle{\displaystyle\omega_{j}}}
    xml-id
    C1.S3.XMD4.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q75&oldid=22259"