DLMF:1.13.E4 (Q468): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10861 / rank
 
Normal rank
Property / Symbols used: Q10861 / qualifier
 
Defining formula:

w 1 ⁢ ( z ) subscript 𝑤 1 𝑧 {\displaystyle{\displaystyle w_{1}(z)}}

w_{1}(z)
Property / Symbols used: Q10861 / qualifier
 
xml-id: C1.S13.XMD5.m1bdec

Revision as of 16:17, 1 January 2020

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DLMF:1.13.E4
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    Statements

    Defining formula
    𝒲 ⁡ { w 1 ⁢ ( z ) , w 2 ⁢ ( z ) } = det ⁡ [ w 1 ⁢ ( z ) w 2 ⁢ ( z ) w 1 ′ ⁢ ( z ) w 2 ′ ⁢ ( z ) ] = w 1 ⁢ ( z ) ⁢ w 2 ′ ⁢ ( z ) - w 2 ⁢ ( z ) ⁢ w 1 ′ ⁢ ( z ) . Wronskian subscript 𝑤 1 𝑧 subscript 𝑤 2 𝑧 subscript 𝑤 1 𝑧 subscript 𝑤 2 𝑧 superscript subscript 𝑤 1 ′ 𝑧 superscript subscript 𝑤 2 ′ 𝑧 subscript 𝑤 1 𝑧 superscript subscript 𝑤 2 ′ 𝑧 subscript 𝑤 2 𝑧 superscript subscript 𝑤 1 ′ 𝑧 {\displaystyle{\displaystyle\mathscr{W}\left\{w_{1}(z),w_{2}(z)\right\}=\det% \begin{bmatrix}w_{1}(z)&w_{2}(z)\\ w_{1}^{\prime}(z)&w_{2}^{\prime}(z)\end{bmatrix}=w_{1}(z)w_{2}^{\prime}(z)-w_{% 2}(z)w_{1}^{\prime}(z).}}
    0 references
    DLMF id
    DLMF:1.13.E4
    0 references
    Symbols used
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3adec
    0 references
    Q10765
    Defining formula
    det {\displaystyle{\displaystyle\det}}
    xml-id
    C1.S3.SS1.m1adec
    0 references
    Q10760
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C1.S1.XMD1.m1cdec
    0 references
    Q10861
    Defining formula
    w 1 ⁢ ( z ) subscript 𝑤 1 𝑧 {\displaystyle{\displaystyle w_{1}(z)}}
    xml-id
    C1.S13.XMD5.m1bdec
    0 references
     
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