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

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Property / constraint
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n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=1,2,3,\dots}}

n=1,2,3,\dots
Property / constraint: n = 1 , 2 , 3 , … 𝑛 1 2 3 … {\displaystyle{\displaystyle n=1,2,3,\dots}} / rank
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Normal rank
Property / Symbols used
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Property / Symbols used: Q11109 / rank
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Normal rank
Property / Symbols used: Q11109 / qualifier
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test:

B n Bernoulli-number-B 𝑛 {\displaystyle{\displaystyle B_{\NVar{n}}}}

\BernoullinumberB{\NVar{n}}
Property / Symbols used: Q11109 / qualifier
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xml-id: C24.S2.SS1.m1aedec
Property / Symbols used
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Property / Symbols used: Hurwitz zeta function / rank
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Normal rank
Property / Symbols used: Hurwitz zeta function / qualifier
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test:

ΞΆ ⁑ ( s , a ) Hurwitz-zeta 𝑠 π‘Ž {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}

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

ΞΆ ⁑ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
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xml-id: C25.S2.E1.m2addec
Property / Symbols used
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Property / Symbols used: principal branch of logarithm function / rank
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Normal rank
Property / Symbols used: principal branch of logarithm function / qualifier
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test:

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

\ln@@{\NVar{z}}
Property / Symbols used: principal branch of logarithm function / qualifier
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xml-id: C4.S2.E2.m2addec
Property / Symbols used
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Property / Symbols used: Q12148 / rank
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Normal rank
Property / Symbols used: Q12148 / qualifier
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test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12148 / qualifier
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xml-id: C25.S1.XMD3.m1ldec

Latest revision as of 12:41, 2 January 2020

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DLMF:25.11.E22
No description defined

    Statements

    test
    ΞΆ β€² ⁑ ( 1 - 2 ⁒ n , 1 2 ) = - B 2 ⁒ n ⁒ ln ⁑ 2 n β‹… 4 n - ( 2 2 ⁒ n - 1 - 1 ) ⁒ ΞΆ β€² ⁑ ( 1 - 2 ⁒ n ) 2 2 ⁒ n - 1 , diffop Hurwitz-zeta 1 1 2 𝑛 1 2 Bernoulli-number-B 2 𝑛 2 β‹… 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
    ΞΆ ⁑ ( s , a ) Hurwitz-zeta 𝑠 π‘Ž {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2awdec
    0 references
    Riemann zeta function
    test
    ΞΆ ⁑ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2addec
    0 references
    principal branch of logarithm function
    test
    ln ⁑ z 𝑧 {\displaystyle{\displaystyle\ln\NVar{z}}}
    xml-id
    C4.S2.E2.m2addec
    0 references
    Q12148
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1ldec
    0 references
     
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