DLMF:1.3.E14 (Q43)

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DLMF:1.3.E14
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    Statements

    DLMF defining formula
    det ⁡ [ 1 a j - b k ] = ( - 1 ) n ⁢ ( n - 1 ) / 2 ⁢ ∏ 1 ≤ j < k ≤ n ( a k - a j ) ⁢ ( b k - b j ) / ∏ j , k = 1 n ( a j - b k ) . delimited-[] 1 subscript 𝑎 𝑗 subscript 𝑏 𝑘 superscript 1 𝑛 𝑛 1 2 subscript product 1 𝑗 𝑘 𝑛 subscript 𝑎 𝑘 subscript 𝑎 𝑗 subscript 𝑏 𝑘 subscript 𝑏 𝑗 subscript superscript product 𝑛 𝑗 𝑘 1 subscript 𝑎 𝑗 subscript 𝑏 𝑘 {\displaystyle{\displaystyle\det\left[\frac{1}{a_{j}-b_{k}}\right]=(-1)^{n(n-1% )/2}\*\prod_{1\leq j<k\leq n}(a_{k}-a_{j})(b_{k}-b_{j})\Bigg{/}\prod^{n}_{j,k=% 1}(a_{j}-b_{k}).}}
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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.m1akdec
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    integer
    DLMF defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C1.S1.XMD3.m1ldec
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    integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C1.S1.XMD4.m1ldec
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    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1fdec
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    Identifiers

     
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