DLMF:10.71.E1 (Q3902): Difference between revisions

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DLMF:10.71.E1
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    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),}}
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    DLMF id
    DLMF:10.71.E1
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