DLMF:1.7.E2 (Q243): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
Property / Symbols used
 
Property / Symbols used: Q10806 / rank
 
Normal rank
Property / Symbols used: Q10806 / qualifier
 
Defining formula:

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

p>1
Property / Symbols used: Q10806 / qualifier
 
xml-id: C1.S7.XMD5.m1dec

Latest revision as of 16:02, 1 January 2020

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DLMF:1.7.E2
No description defined

    Statements

    Defining formula
    ∑ j = 1 n a j ⁢ b j ≤ ( ∑ j = 1 n a j p ) 1 / p ⁢ ( ∑ j = 1 n b j q ) 1 / q . subscript superscript 𝑛 𝑗 1 subscript 𝑎 𝑗 subscript 𝑏 𝑗 superscript subscript superscript 𝑛 𝑗 1 superscript subscript 𝑎 𝑗 𝑝 1 𝑝 superscript subscript superscript 𝑛 𝑗 1 superscript subscript 𝑏 𝑗 𝑞 1 𝑞 {\displaystyle{\displaystyle\sum^{n}_{j=1}a_{j}b_{j}\leq\left(\sum^{n}_{j=1}a_% {j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}.}}
    0 references
    DLMF id
    DLMF:1.7.E2
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    Q10763
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C1.S1.XMD3.m1adec
    0 references
    Q10757
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C1.S1.XMD7.m1adec
    0 references
    Q10805
    Defining formula
    q 𝑞 {\displaystyle{\displaystyle q}}
    xml-id
    C1.S7.XMD4.m1dec
    0 references
    Q10806
    Defining formula
    p > 1 𝑝 1 {\displaystyle{\displaystyle p>1}}
    xml-id
    C1.S7.XMD5.m1dec
    0 references
     
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