DLMF:1.8.E5 (Q259): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(One intermediate revision by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3abdec
Property / Symbols used
 
Property / Symbols used: Q10757 / rank
 
Normal rank
Property / Symbols used: Q10757 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q10757 / qualifier
 
xml-id: C1.S1.XMD7.m1ddec

Latest revision as of 16:03, 1 January 2020

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DLMF:1.8.E5
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    Statements

    1 2 a 0 2 + n = 1 ( a n 2 + b n 2 ) 1 π - π π ( f ( x ) ) 2 d x . 1 2 superscript subscript 𝑎 0 2 subscript superscript 𝑛 1 superscript subscript 𝑎 𝑛 2 superscript subscript 𝑏 𝑛 2 1 𝜋 subscript superscript 𝜋 𝜋 superscript 𝑓 𝑥 2 𝑥 {\displaystyle{\displaystyle\tfrac{1}{2}a_{0}^{2}+\sum^{\infty}_{n=1}(a_{n}^{2% }+b_{n}^{2})\leq\frac{1}{\pi}\int^{\pi}_{-\pi}(f(x))^{2}\mathrm{d}x.}}
    0 references
    DLMF:1.8.E5
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2abdec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1abdec
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    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3abdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C1.S1.XMD7.m1ddec
    0 references