DLMF:25.2.E6 (Q7601): 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.m2addec
Property / Symbols used
 
Property / Symbols used: principal branch of logarithm function / rank
 
Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
 
Defining formula:

ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
 
xml-id: C4.S2.E2.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.m1acdec
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.m1edec
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.m1ddec

Latest revision as of 13:21, 2 January 2020

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English
DLMF:25.2.E6
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    Statements

    ζ ( s ) = - n = 2 ( ln n ) n - s , diffop Riemann-zeta 1 𝑠 superscript subscript 𝑛 2 𝑛 superscript 𝑛 𝑠 {\displaystyle{\displaystyle\zeta'\left(s\right)=-\sum_{n=2}^{\infty}(\ln n)n^% {-s},}}
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    DLMF:25.2.E6
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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.m2addec
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    ln z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    C4.S2.E2.m2aadec
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    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1acdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C25.S1.XMD3.m1edec
    0 references
    s 𝑠 {\displaystyle{\displaystyle s}}
    C25.S1.XMD7.m1ddec
    0 references