DLMF:10.71.E2 (Q3903)

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DLMF:10.71.E2
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    test
    ∫ 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:10.71.E2
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