DLMF:24.9.E10 (Q7506): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m2afdec

Revision as of 01:39, 2 January 2020

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DLMF:24.9.E10
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    Statements

    Defining formula
    4 n + 1 ⁢ ( 2 ⁢ n ) ! π 2 ⁢ n + 1 > ( - 1 ) n ⁢ E 2 ⁢ n > 4 n + 1 ⁢ ( 2 ⁢ n ) ! π 2 ⁢ n + 1 ⁢ 1 1 + 3 - 1 - 2 ⁢ n . superscript 4 𝑛 1 2 𝑛 superscript 𝜋 2 𝑛 1 superscript 1 𝑛 Euler-number-E 2 𝑛 superscript 4 𝑛 1 2 𝑛 superscript 𝜋 2 𝑛 1 1 1 superscript 3 1 2 𝑛 {\displaystyle{\displaystyle\frac{4^{n+1}(2n)!}{\pi^{2n+1}}>(-1)^{n}E_{2n}>% \frac{4^{n+1}(2n)!}{\pi^{2n+1}}\frac{1}{1+3^{-1-2n}}.}}
    0 references
    DLMF id
    DLMF:24.9.E10
    0 references
    Symbols used
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1abdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2afdec
    0 references
     
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