DLMF:25.2.E2 (Q7597): Difference between revisions

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Changed an Item: Add constraint
 
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Property / constraint
 

s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}

\realpart@@{s}>1
Property / constraint: s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}} / rank
 
Normal rank
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.m2aadec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
Defining formula:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1adec
Property / Symbols used
 
Property / Symbols used: Q12148 / rank
 
Normal rank
Property / Symbols used: Q12148 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12148 / qualifier
 
xml-id: C25.S1.XMD3.m1adec
Property / Symbols used
 
Property / Symbols used: Q12149 / rank
 
Normal rank
Property / Symbols used: Q12149 / qualifier
 
Defining formula:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q12149 / qualifier
 
xml-id: C25.S1.XMD7.m1adec

Latest revision as of 13:20, 2 January 2020

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DLMF:25.2.E2
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    Statements

    ζ ( s ) = 1 1 - 2 - s n = 0 1 ( 2 n + 1 ) s , Riemann-zeta 𝑠 1 1 superscript 2 𝑠 superscript subscript 𝑛 0 1 superscript 2 𝑛 1 𝑠 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{1}{1-2^{-s}}\sum_{n=0}^{% \infty}\frac{1}{(2n+1)^{s}},}}
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    DLMF:25.2.E2
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    s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    C25.S2.E1.m2aadec
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    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1adec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C25.S1.XMD3.m1adec
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    s 𝑠 {\displaystyle{\displaystyle s}}
    C25.S1.XMD7.m1adec
    0 references