DLMF:10.71.E7 (Q3908)

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DLMF:10.71.E7
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    ∫ x ⁢ ( f ν 2 - g ν 2 ) ⁢ d x = 1 2 ⁢ x 2 ⁢ ( f ν 2 - f ν - 1 ⁢ f ν + 1 - g ν 2 + g ν - 1 ⁢ g ν + 1 ) . 𝑥 superscript subscript 𝑓 𝜈 2 superscript subscript 𝑔 𝜈 2 𝑥 1 2 superscript 𝑥 2 superscript subscript 𝑓 𝜈 2 subscript 𝑓 𝜈 1 subscript 𝑓 𝜈 1 superscript subscript 𝑔 𝜈 2 subscript 𝑔 𝜈 1 subscript 𝑔 𝜈 1 {\displaystyle{\displaystyle\int x(f_{\nu}^{2}-g_{\nu}^{2})\mathrm{d}x=\tfrac{% 1}{2}x^{2}\left(f_{\nu}^{2}-f_{\nu-1}f_{\nu+1}-g_{\nu}^{2}+g_{\nu-1}g_{\nu+1}% \right).}}
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    DLMF:10.71.E7
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