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

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Property / Symbols used
 
Property / Symbols used: Hurwitz zeta function / rank
 
Normal rank
Property / Symbols used: Hurwitz zeta function / qualifier
 
test:

ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}

\Hurwitzzeta@{\NVar{s}}{\NVar{a}}
Property / Symbols used: Hurwitz zeta function / qualifier
 
xml-id: C25.S11.E1.m2awdec

Revision as of 12:40, 2 January 2020

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DLMF:25.11.E22
No description defined

    Statements

    test
    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
    test
    B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}
    xml-id
    C24.S2.SS1.m1aedec
    0 references
    Hurwitz zeta function
    test
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2awdec
    0 references
     
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