DLMF:25.11.E41 (Q7715): 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: 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.m2aidec
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.m1afdec
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.m1zdec

Latest revision as of 13:46, 2 January 2020

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DLMF:25.11.E41
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    Statements

    ζ ( s , a + 1 ) = ζ ( s ) - s ζ ( s + 1 ) a + O ( a 2 ) . Hurwitz-zeta 𝑠 𝑎 1 Riemann-zeta 𝑠 𝑠 Riemann-zeta 𝑠 1 𝑎 Big-O superscript 𝑎 2 {\displaystyle{\displaystyle\zeta\left(s,a+1\right)=\zeta\left(s\right)-s\zeta% \left(s+1\right)a+O\left(a^{2}\right).}}
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    DLMF:25.11.E41
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    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2aadec
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    ζ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    C25.S11.E1.m2aandec
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    ζ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    C25.S2.E1.m2aidec
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    a 𝑎 {\displaystyle{\displaystyle a}}
    C25.S1.XMD6.m1afdec
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    s 𝑠 {\displaystyle{\displaystyle s}}
    C25.S1.XMD7.m1zdec
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