DLMF:24.11.E1 (Q7516): Difference between revisions

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Property / constraint
 

n 𝑛 {\displaystyle{\displaystyle n\to\infty}}

n\to\infty
Property / constraint: n 𝑛 {\displaystyle{\displaystyle n\to\infty}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q11109 / rank
 
Normal rank
Property / Symbols used: Q11109 / qualifier
 
Defining formula:

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

\BernoullinumberB{\NVar{n}}
Property / Symbols used: Q11109 / qualifier
 
xml-id: C24.S2.SS1.m1adec
Property / Symbols used
 
Property / Symbols used: asymptotic equality / rank
 
Normal rank
Property / Symbols used: asymptotic equality / qualifier
 
Defining formula:

asymptotically-equals {\displaystyle{\displaystyle\sim}}

\asympeq
Property / Symbols used: asymptotic equality / qualifier
 
xml-id: C2.S1.E1.m2adec
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.m2adec
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.m5adec
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.m1dec

Latest revision as of 01:41, 2 January 2020

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English
DLMF:24.11.E1
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    Statements

    ( - 1 ) n + 1 B 2 n 2 ( 2 n ) ! ( 2 π ) 2 n , asymptotically-equals superscript 1 𝑛 1 Bernoulli-number-B 2 𝑛 2 2 𝑛 superscript 2 𝜋 2 𝑛 {\displaystyle{\displaystyle(-1)^{n+1}B_{2n}\sim\frac{2(2n)!}{(2\pi)^{2n}},}}
    0 references
    DLMF:24.11.E1
    0 references
    n 𝑛 {\displaystyle{\displaystyle n\to\infty}}
    0 references
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    C24.S2.SS1.m1adec
    0 references
    asymptotically-equals {\displaystyle{\displaystyle\sim}}
    C2.S1.E1.m2adec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    ! {\displaystyle{\displaystyle!}}
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C24.S1.XMD5.m1dec
    0 references