DLMF:25.16.E10 (Q7766): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q12169 / rank
 
Normal rank
Property / Symbols used: Q12169 / qualifier
 
Defining formula:

H ( s ) Euler-sum-H 𝑠 {\displaystyle{\displaystyle H\left(\NVar{s}\right)}}

\EulersumH@{\NVar{s}}
Property / Symbols used: Q12169 / qualifier
 
xml-id: C25.S16.SS2.p1.m1aedec
Property / Symbols used
 
Property / Symbols used: Riemann zeta function / rank
 
Normal rank
Property / Symbols used: Riemann zeta function / qualifier
 
Defining formula:

ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
 
xml-id: C25.S2.E1.m2aedec
Property / Symbols used
 
Property / Symbols used: Q12161 / rank
 
Normal rank
Property / Symbols used: Q12161 / qualifier
 
Defining formula:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q12161 / qualifier
 
xml-id: C25.S1.XMD6.m1adec

Latest revision as of 01:07, 2 January 2020

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DLMF:25.16.E10
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    Statements

    H ( - 2 a ) = 1 2 ζ ( 1 - 2 a ) = - B 2 a 4 a , Euler-sum-H 2 𝑎 1 2 Riemann-zeta 1 2 𝑎 Bernoulli-number-B 2 𝑎 4 𝑎 {\displaystyle{\displaystyle H\left(-2a\right)=\frac{1}{2}\zeta\left(1-2a% \right)=-\frac{B_{2a}}{4a},}}
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    DLMF:25.16.E10
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    a = 1 , 2 , 3 , 𝑎 1 2 3 {\displaystyle{\displaystyle a=1,2,3,\dots}}
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    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    C24.S2.SS1.m1adec
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    H ( s ) Euler-sum-H 𝑠 {\displaystyle{\displaystyle H\left(\NVar{s}\right)}}
    C25.S16.SS2.p1.m1aedec
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    ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    C25.S2.E1.m2aedec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C25.S1.XMD6.m1adec
    0 references