DLMF:24.9.E8 (Q7504): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(4 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q11109 / rank
 
Normal rank
Property / Symbols used: Q11109 / qualifier
 
test:

B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}

\BernoullinumberB{\NVar{n}}
Property / Symbols used: Q11109 / qualifier
 
xml-id: C24.S2.SS1.m1acdec
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
 
test:

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.m2addec
Property / Symbols used
 
Property / Symbols used: Q10755 / rank
 
Normal rank
Property / Symbols used: Q10755 / qualifier
 
test:

! {\displaystyle{\displaystyle!}}

!
Property / Symbols used: Q10755 / qualifier
 
xml-id: introduction.Sx4.p1.t1.r15.m5abdec
Property / Symbols used
 
Property / Symbols used: Q12110 / rank
 
Normal rank
Property / Symbols used: Q12110 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12110 / qualifier
 
xml-id: C24.S1.XMD5.m1gdec
Property / Symbols used
 
Property / Symbols used: Q12120 / rank
 
Normal rank
Property / Symbols used: Q12120 / qualifier
 
test:

β 𝛽 {\displaystyle{\displaystyle\beta}}

\beta
Property / Symbols used: Q12120 / qualifier
 
xml-id: C24.S9.XMD1.m1dec

Latest revision as of 00:39, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:24.9.E8
No description defined

    Statements

    test
    2 ⁢ ( 2 ⁢ n ) ! ( 2 ⁢ π ) 2 ⁢ n ⁢ 1 1 - 2 β - 2 ⁢ n ≥ ( - 1 ) n + 1 ⁢ B 2 ⁢ n ≥ 2 ⁢ ( 2 ⁢ n ) ! ( 2 ⁢ π ) 2 ⁢ n ⁢ 1 1 - 2 - 2 ⁢ n 2 2 𝑛 superscript 2 𝜋 2 𝑛 1 1 superscript 2 𝛽 2 𝑛 superscript 1 𝑛 1 Bernoulli-number-B 2 𝑛 2 2 𝑛 superscript 2 𝜋 2 𝑛 1 1 superscript 2 2 𝑛 {\displaystyle{\displaystyle\frac{2(2n)!}{(2\pi)^{2n}}\frac{1}{1-2^{\beta-2n}}% \geq(-1)^{n+1}B_{2n}\geq\frac{2(2n)!}{(2\pi)^{2n}}\frac{1}{1-2^{-2n}}}}
    0 references
    DLMF id
    DLMF:24.9.E8
    0 references
    Symbols used
    Q11109
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    Q10755
    test
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    0 references
    Q12110
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1gdec
    0 references
    Q12120
    test
    β 𝛽 {\displaystyle{\displaystyle\beta}}
    xml-id
    C24.S9.XMD1.m1dec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q7504&oldid=41950"