DLMF:1.7.E5 (Q246): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q10808 / rank
 
Normal rank
Property / Symbols used: Q10808 / qualifier
 
test:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q10808 / qualifier
 
xml-id: C1.S7.XMD9.m1dec

Latest revision as of 15:02, 1 January 2020

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English
DLMF:1.7.E5
No description defined

    Statements

    test
    ∫ a b f ⁢ ( x ) ⁢ g ⁢ ( x ) ⁢ d x ≤ ( ∫ a b ( f ⁢ ( x ) ) p ⁢ d x ) 1 / p ⁢ ( ∫ a b ( g ⁢ ( x ) ) q ⁢ d x ) 1 / q . superscript subscript 𝑎 𝑏 𝑓 𝑥 𝑔 𝑥 𝑥 superscript superscript subscript 𝑎 𝑏 superscript 𝑓 𝑥 𝑝 𝑥 1 𝑝 superscript superscript subscript 𝑎 𝑏 superscript 𝑔 𝑥 𝑞 𝑥 1 𝑞 {\displaystyle{\displaystyle\int_{a}^{b}f(x)g(x)\mathrm{d}x\leq\left(\int_{a}^% {b}(f(x))^{p}\mathrm{d}x\right)^{1/p}\left(\int_{a}^{b}(g(x))^{q}\mathrm{d}x% \right)^{1/q}.}}
    0 references
    DLMF id
    DLMF:1.7.E5
    0 references
    Symbols used
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    Q10771
    test
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3aadec
    0 references
    Q10807
    test
    p > 1 𝑝 1 {\displaystyle{\displaystyle p>1}}
    xml-id
    C1.S7.XMD10.m1dec
    0 references
    Q10808
    test
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C1.S7.XMD9.m1dec
    0 references
     
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