DLMF:24.4.E19 (Q7432): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11288 / rank
 
Normal rank
Property / Symbols used: Q11288 / qualifier
 
test:

B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}

\BernoullipolyB{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q11288 / qualifier
 
xml-id: C24.S2.SS1.m2agdec
Property / Symbols used
 
Property / Symbols used: Q12114 / rank
 
Normal rank
Property / Symbols used: Q12114 / qualifier
 
test:

E n ⁡ ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}

\EulerpolyE{\NVar{n}}@{\NVar{x}}
Property / Symbols used: Q12114 / qualifier
 
xml-id: C24.S2.SS2.m2agdec
Property / Symbols used
 
Property / Symbols used: Q12113 / rank
 
Normal rank
Property / Symbols used: Q12113 / qualifier
 
test:

k 𝑘 {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12113 / qualifier
 
xml-id: C24.S1.XMD2.m1ldec
Property / Symbols used
 
Property / Symbols used: Q12115 / rank
 
Normal rank
Property / Symbols used: Q12115 / qualifier
 
test:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12115 / qualifier
 
xml-id: C24.S1.XMD4.m1fdec
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.m1rdec
Property / Symbols used
 
Property / Symbols used: Q12112 / rank
 
Normal rank
Property / Symbols used: Q12112 / qualifier
 
test:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12112 / qualifier
 
xml-id: C24.S1.XMD7.m1jdec

Latest revision as of 00:27, 2 January 2020

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English
DLMF:24.4.E19
No description defined

    Statements

    test
    E n ⁡ ( m ⁢ x ) = - 2 ⁢ m n n + 1 ⁢ ∑ k = 0 m - 1 ( - 1 ) k ⁢ B n + 1 ⁡ ( x + k m ) , Euler-polynomial-E 𝑛 𝑚 𝑥 2 superscript 𝑚 𝑛 𝑛 1 superscript subscript 𝑘 0 𝑚 1 superscript 1 𝑘 Bernoulli-polynomial-B 𝑛 1 𝑥 𝑘 𝑚 {\displaystyle{\displaystyle E_{n}\left(mx\right)=-\frac{2m^{n}}{n+1}\sum_{k=0% }^{m-1}(-1)^{k}B_{n+1}\left(x+\frac{k}{m}\right),}}
    0 references
    DLMF id
    DLMF:24.4.E19
    0 references
    constraint
    m = 2 , 4 , 6 , … 𝑚 2 4 6 … {\displaystyle{\displaystyle m=2,4,6,\dots}}
    0 references
    Symbols used
    Q11288
    test
    B n ⁡ ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS1.m2agdec
    0 references
    Q12114
    test
    E n ⁡ ( x ) Euler-polynomial-E 𝑛 𝑥 {\displaystyle{\displaystyle E_{\NVar{n}}\left(\NVar{x}\right)}}
    xml-id
    C24.S2.SS2.m2agdec
    0 references
    Q12113
    test
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C24.S1.XMD2.m1ldec
    0 references
    Q12115
    test
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C24.S1.XMD4.m1fdec
    0 references
    Q12110
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C24.S1.XMD5.m1rdec
    0 references
    Q12112
    test
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C24.S1.XMD7.m1jdec
    0 references
     
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