DLMF:24.4.E7 (Q7420): 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.m2acdec
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.m1dec
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.m1dec
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.m1fdec

Latest revision as of 00:25, 2 January 2020

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DLMF:24.4.E7
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    Statements

    k = 1 m k n = B n + 1 ( m + 1 ) - B n + 1 n + 1 , superscript subscript 𝑘 1 𝑚 superscript 𝑘 𝑛 Bernoulli-polynomial-B 𝑛 1 𝑚 1 Bernoulli-number-B 𝑛 1 𝑛 1 {\displaystyle{\displaystyle\sum_{k=1}^{m}k^{n}=\frac{B_{n+1}\left(m+1\right)-% B_{n+1}}{n+1},}}
    0 references
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    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    C24.S2.SS1.m1adec
    0 references
    B n ( x ) Bernoulli-polynomial-B 𝑛 𝑥 {\displaystyle{\displaystyle B_{\NVar{n}}\left(\NVar{x}\right)}}
    C24.S2.SS1.m2acdec
    0 references
    k 𝑘 {\displaystyle{\displaystyle k}}
    C24.S1.XMD2.m1dec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C24.S1.XMD4.m1dec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C24.S1.XMD5.m1fdec
    0 references