DLMF:25.2.E7 (Q7602): Difference between revisions

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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.m1fdec
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.m1edec

Latest revision as of 13:21, 2 January 2020

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DLMF:25.2.E7
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    Statements

    Defining formula
    ζ ( k ) ⁡ ( s ) = ( - 1 ) k ⁢ ∑ n = 2 ∞ ( ln ⁡ n ) k ⁢ n - s , Riemann-zeta 𝑘 𝑠 superscript 1 𝑘 superscript subscript 𝑛 2 superscript 𝑛 𝑘 superscript 𝑛 𝑠 {\displaystyle{\displaystyle{\zeta^{(k)}}\left(s\right)=(-1)^{k}\sum_{n=2}^{% \infty}(\ln n)^{k}n^{-s},}}
    0 references
    DLMF id
    DLMF:25.2.E7
    0 references
    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
    0 references
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
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    k = 1 , 2 , 3 , … 𝑘 1 2 3 … {\displaystyle{\displaystyle k=1,2,3,\dots}}
    0 references
    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aedec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2abdec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1addec
    0 references
    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1adec
    0 references
    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1fdec
    0 references
    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1edec
    0 references
     
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