DLMF:24.4.E16 (Q7429): Difference between revisions

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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.m1addec
Property / Symbols used
 
Property / Symbols used: Q11238 / rank
 
Normal rank
Property / Symbols used: Q11238 / qualifier
 
Defining formula:

E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}

\EulernumberE{\NVar{n}}
Property / Symbols used: Q11238 / qualifier
 
xml-id: C24.S2.SS2.m1aadec
Property / Symbols used
 
Property / Symbols used: Q10754 / rank
 
Normal rank
Property / Symbols used: Q10754 / qualifier
 
Defining formula:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10754 / qualifier
 
xml-id: C1.S2.SS1.m1aedec
Property / Symbols used
 
Property / Symbols used: Q12113 / rank
 
Normal rank
Property / Symbols used: Q12113 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12113 / qualifier
 
xml-id: C24.S1.XMD2.m1idec
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.m1odec

Latest revision as of 01:26, 2 January 2020

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DLMF:24.4.E16
No description defined

    Statements

    Defining formula
    E 2 ⁢ n = 1 2 ⁢ n + 1 - ∑ k = 1 n ( 2 ⁢ n 2 ⁢ k - 1 ) ⁢ 2 2 ⁢ k ⁢ ( 2 2 ⁢ k - 1 - 1 ) ⁢ B 2 ⁢ k k , Euler-number-E 2 𝑛 1 2 𝑛 1 superscript subscript 𝑘 1 𝑛 binomial 2 𝑛 2 𝑘 1 superscript 2 2 𝑘 superscript 2 2 𝑘 1 1 Bernoulli-number-B 2 𝑘 𝑘 {\displaystyle{\displaystyle E_{2n}=\frac{1}{2n+1}-\sum_{k=1}^{n}{2n\choose 2k% -1}\frac{2^{2k}(2^{2k-1}-1)B_{2k}}{k},}}
    0 references
    DLMF id
    DLMF:24.4.E16
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1addec
    0 references
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1aadec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aedec
    0 references
    Q12113
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1idec
    0 references
    Q12110
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1odec
    0 references
     
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