DLMF:24.9.E5 (Q7501): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
Defining formula:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5aadec
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12112 / rank
 
Normal rank
Property / Symbols used: Q12112 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12112 / qualifier
 
xml-id: C24.S1.XMD7.m1ddec

Latest revision as of 01:38, 2 January 2020

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DLMF:24.9.E5
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    Statements

    4 ( 2 n - 1 ) ! π 2 n 2 2 n - 1 2 2 n - 2 > ( - 1 ) n E 2 n - 1 ( x ) > 0 . 4 2 𝑛 1 superscript 𝜋 2 𝑛 superscript 2 2 𝑛 1 superscript 2 2 𝑛 2 superscript 1 𝑛 Euler-polynomial-E 2 𝑛 1 𝑥 0 {\displaystyle{\displaystyle\frac{4(2n-1)!}{\pi^{2n}}\frac{2^{2n}-1}{2^{2n}-2}% >(-1)^{n}E_{2n-1}\left(x\right)>0.}}
    0 references
    DLMF:24.9.E5
    0 references
    E n ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    C24.S2.SS2.m2aadec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C24.S1.XMD5.m1ddec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C24.S1.XMD7.m1ddec
    0 references