DLMF:1.7.E6 (Q247): Difference between revisions

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imported>Admin
 
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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.m1abdec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
test:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: Q10807 / rank
 
Normal rank
Property / Symbols used: Q10807 / qualifier
 
test:

p > 1 𝑝 1 {\displaystyle{\displaystyle p>1}}

p>1
Property / Symbols used: Q10807 / qualifier
 
xml-id: C1.S7.XMD10.m1adec

Latest revision as of 15:02, 1 January 2020

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DLMF:1.7.E6
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    Statements

    ( a b ( f ( x ) + g ( x ) ) p d x ) 1 / p ( a b ( f ( x ) ) p d x ) 1 / p + ( a b ( g ( x ) ) p d x ) 1 / p . superscript superscript subscript 𝑎 𝑏 superscript 𝑓 𝑥 𝑔 𝑥 𝑝 𝑥 1 𝑝 superscript superscript subscript 𝑎 𝑏 superscript 𝑓 𝑥 𝑝 𝑥 1 𝑝 superscript superscript subscript 𝑎 𝑏 superscript 𝑔 𝑥 𝑝 𝑥 1 𝑝 {\displaystyle{\displaystyle\left(\int_{a}^{b}(f(x)+g(x))^{p}\mathrm{d}x\right% )^{1/p}\leq\left(\int_{a}^{b}(f(x))^{p}\mathrm{d}x\right)^{1/p}+\left(\int_{a}% ^{b}(g(x))^{p}\mathrm{d}x\right)^{1/p}.}}
    0 references
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1abdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3abdec
    0 references
    p > 1 𝑝 1 {\displaystyle{\displaystyle p>1}}
    C1.S7.XMD10.m1adec
    0 references