DLMF:3.6.E7 (Q1312): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: coefficient (locally) / rank
 
Normal rank
Property / Symbols used: coefficient (locally) / qualifier
 
Defining formula:

c n subscript 𝑐 𝑛 {\displaystyle{\displaystyle c_{n}}}

c_{n}
Property / Symbols used: coefficient (locally) / qualifier
 
xml-id: C3.S6.XMD4.m1cdec

Revision as of 17:54, 1 January 2020

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DLMF:3.6.E7
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    Statements

    Defining formula
    [ - b 1 a 1 0 c 2 - b 2 a 2 ⋱ ⋱ ⋱ c N - 2 - b N - 2 a N - 2 0 c N - 1 - b N - 1 ] ⁢ [ w 1 ( N ) w 2 ( N ) ⋮ w N - 2 ( N ) w N - 1 ( N ) ] = [ d 1 - c 1 ⁢ λ d 2 ⋮ d N - 2 d N - 1 ] . subscript 𝑏 1 subscript 𝑎 1 absent absent 0 subscript 𝑐 2 subscript 𝑏 2 subscript 𝑎 2 absent ⋱ ⋱ ⋱ absent absent subscript 𝑐 𝑁 2 subscript 𝑏 𝑁 2 subscript 𝑎 𝑁 2 0 absent absent subscript 𝑐 𝑁 1 subscript 𝑏 𝑁 1 superscript subscript 𝑤 1 𝑁 superscript subscript 𝑤 2 𝑁 ⋮ superscript subscript 𝑤 𝑁 2 𝑁 superscript subscript 𝑤 𝑁 1 𝑁 subscript 𝑑 1 subscript 𝑐 1 𝜆 subscript 𝑑 2 ⋮ subscript 𝑑 𝑁 2 subscript 𝑑 𝑁 1 {\displaystyle{\displaystyle\begin{bmatrix}-b_{1}&a_{1}&&&0\\ c_{2}&-b_{2}&a_{2}\\ &\ddots&\ddots&\ddots\\ &&c_{N-2}&-b_{N-2}&a_{N-2}\\ 0&&&c_{N-1}&-b_{N-1}\end{bmatrix}\begin{bmatrix}w_{1}^{(N)}\\ w_{2}^{(N)}\\ \vdots\\ w_{N-2}^{(N)}\\ w_{N-1}^{(N)}\end{bmatrix}=\begin{bmatrix}d_{1}-c_{1}\lambda\\ d_{2}\\ \vdots\\ d_{N-2}\\ d_{N-1}\end{bmatrix}.}}
    0 references
    DLMF id
    DLMF:3.6.E7
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    Q11179
    Defining formula
    w n subscript 𝑤 𝑛 {\displaystyle{\displaystyle w_{n}}}
    xml-id
    C3.S6.XMD1.m1fdec
    0 references
    Q11182
    Defining formula
    N 𝑁 {\displaystyle{\displaystyle N}}
    xml-id
    C3.S6.XMD10.m1dec
    0 references
    coefficient (locally)
    Defining formula
    a n subscript 𝑎 𝑛 {\displaystyle{\displaystyle a_{n}}}
    xml-id
    C3.S6.XMD2.m1cdec
    0 references
    coefficient (locally)
    Defining formula
    b n subscript 𝑏 𝑛 {\displaystyle{\displaystyle b_{n}}}
    xml-id
    C3.S6.XMD3.m1cdec
    0 references
    coefficient (locally)
    Defining formula
    c n subscript 𝑐 𝑛 {\displaystyle{\displaystyle c_{n}}}
    xml-id
    C3.S6.XMD4.m1cdec
    0 references
     
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