DLMF:10.71.E7 (Q3908): Difference between revisions

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imported>Admin
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
test:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1afdec

Revision as of 14:34, 2 January 2020

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DLMF:10.71.E7
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    Statements

    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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    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1afdec
    0 references