DLMF:10.71.E7 (Q3908)

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DLMF:10.71.E7
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    Statements

    test
    ∫ 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).}}
    0 references
    DLMF id
    DLMF:10.71.E7
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
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    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3afdec
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    Q11435
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C10.S1.XMD4.m1fdec
    0 references
    Q11427
    test
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1fdec
    0 references
    Q11487
    test
    f ν subscript 𝑓 𝜈 {\displaystyle{\displaystyle f_{\nu}}}
    xml-id
    C10.S63.XMD1.m1fdec
    0 references
    Q11488
    test
    g ν subscript 𝑔 𝜈 {\displaystyle{\displaystyle g_{\nu}}}
    xml-id
    C10.S63.XMD2.m1fdec
    0 references
     
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