DLMF:24.6.E10 (Q7474): Difference between revisions

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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.m1acdec
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.m1aidec
Property / Symbols used
 
Property / Symbols used: Q12116 / rank
 
Normal rank
Property / Symbols used: Q12116 / qualifier
 
Defining formula:

j 𝑗 {\displaystyle{\displaystyle j}}

j
Property / Symbols used: Q12116 / qualifier
 
xml-id: C24.S1.XMD1.m1idec
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.m1idec

Latest revision as of 01:32, 2 January 2020

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DLMF:24.6.E10
No description defined

    Statements

    Defining formula
    E n = 1 2 n ⁢ ∑ k = 1 n + 1 ( n + 1 k ) ⁢ ∑ j = 0 k - 1 ( - 1 ) j ⁢ ( 2 ⁢ j + 1 ) n . Euler-number-E 𝑛 1 superscript 2 𝑛 superscript subscript 𝑘 1 𝑛 1 binomial 𝑛 1 𝑘 superscript subscript 𝑗 0 𝑘 1 superscript 1 𝑗 superscript 2 𝑗 1 𝑛 {\displaystyle{\displaystyle E_{n}=\frac{1}{2^{n}}\sum_{k=1}^{n+1}{n+1\choose k% }\sum_{j=0}^{k-1}(-1)^{j}(2j+1)^{n}.}}
    0 references
    DLMF id
    DLMF:24.6.E10
    0 references
    Symbols used
    Q11238
    Defining formula
    E n Euler-number-E 𝑛 {\displaystyle{\displaystyle E_{\NVar{n}}}}
    xml-id
    C24.S2.SS2.m1acdec
    0 references
    Q10754
    Defining formula
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    xml-id
    C1.S2.SS1.m1aidec
    0 references
    Q12116
    Defining formula
    j 𝑗 {\displaystyle{\displaystyle j}}
    xml-id
    C24.S1.XMD1.m1idec
    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.m1idec
    0 references
     
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