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

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Property / Symbols used
 
Property / Symbols used: Q12114 / rank
 
Normal rank
Property / Symbols used: Q12114 / qualifier
 
Defining formula:

E n ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}

\EulerpolyE{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q12114 / qualifier
 
xml-id: C24.S2.SS2.m2aadec

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.}}
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    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