DLMF:25.11.E22 (Q7696): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
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.m1ldec

Latest revision as of 13:41, 2 January 2020

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DLMF:25.11.E22
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    Statements

    Defining formula
    ζ ′ ⁡ ( 1 - 2 ⁢ n , 1 2 ) = - B 2 ⁢ n ⁢ ln ⁡ 2 n ⋅ 4 n - ( 2 2 ⁢ n - 1 - 1 ) ⁢ ζ ′ ⁡ ( 1 - 2 ⁢ n ) 2 2 ⁢ n - 1 , diffop Hurwitz-zeta 1 1 2 𝑛 1 2 Bernoulli-number-B 2 𝑛 2 ⋅ 𝑛 superscript 4 𝑛 superscript 2 2 𝑛 1 1 diffop Riemann-zeta 1 1 2 𝑛 superscript 2 2 𝑛 1 {\displaystyle{\displaystyle\zeta'\left(1-2n,\tfrac{1}{2}\right)=-\frac{B_{2n}% \ln 2}{n\cdot 4^{n}}-\frac{(2^{2n-1}-1)\zeta'\left(1-2n\right)}{2^{2n-1}},}}
    0 references
    DLMF id
    DLMF:25.11.E22
    0 references
    constraint
    n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=1,2,3,\dots}}
    0 references
    Symbols used
    Q11109
    Defining formula
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aedec
    0 references
    Hurwitz zeta function
    Defining formula
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2awdec
    0 references
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2addec
    0 references
    principal branch of logarithm function
    Defining formula
    ln ⁡ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2addec
    0 references
    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1ldec
    0 references
     
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