DLMF:10.71.E1 (Q3902)

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DLMF:10.71.E1
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    Statements

    Defining formula
    ∫ x 1 + ν ⁢ f ν ⁢ d x = - x 1 + ν 2 ⁢ ( f ν + 1 - g ν + 1 ) = - x 1 + ν ⁢ ( ν x ⁢ g ν - g ν ′ ) , superscript 𝑥 1 𝜈 subscript 𝑓 𝜈 𝑥 superscript 𝑥 1 𝜈 2 subscript 𝑓 𝜈 1 subscript 𝑔 𝜈 1 superscript 𝑥 1 𝜈 𝜈 𝑥 subscript 𝑔 𝜈 superscript subscript 𝑔 𝜈 ′ {\displaystyle{\displaystyle\int x^{1+\nu}f_{\nu}\mathrm{d}x=-\frac{x^{1+\nu}}% {\sqrt{2}}(f_{\nu+1}-g_{\nu+1})=-x^{1+\nu}\left(\frac{\nu}{x}g_{\nu}-g_{\nu}^{% \prime}\right),}}
    0 references
    DLMF id
    DLMF:10.71.E1
    0 references
    Symbols used
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11435
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1dec
    0 references
    Q11427
    Defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1dec
    0 references
    Q11487
    Defining formula
    f ν subscript 𝑓 𝜈 {\displaystyle{\displaystyle f_{\nu}}}
    xml-id
    C10.S63.XMD1.m1dec
    0 references
     
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