DLMF:25.6.E18 (Q7655): Difference between revisions

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Property / constraint
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n β‰₯ 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}

n\geq 1
Property / constraint: n β‰₯ 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}} / rank
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Normal rank
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.m2aqdec

Latest revision as of 12:32, 2 January 2020

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DLMF:25.6.E18
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    Statements

    test
    ( n + 1 4 ) ⁒ ΞΆ ⁑ ( 4 ⁒ n ) + 1 2 ⁒ ( ΞΆ ⁑ ( 2 ⁒ n ) ) 2 = βˆ‘ k = 1 n ΞΆ ⁑ ( 2 ⁒ k ) ⁒ ΞΆ ⁑ ( 4 ⁒ n - 2 ⁒ k ) , 𝑛 1 4 Riemann-zeta 4 𝑛 1 2 superscript Riemann-zeta 2 𝑛 2 superscript subscript π‘˜ 1 𝑛 Riemann-zeta 2 π‘˜ Riemann-zeta 4 𝑛 2 π‘˜ {\displaystyle{\displaystyle{\left(n+\tfrac{1}{4}\right)\zeta\left(4n\right)+% \tfrac{1}{2}(\zeta\left(2n\right))^{2}=\sum_{k=1}^{n}\zeta\left(2k\right)\zeta% \left(4n-2k\right)},}}
    0 references
    DLMF id
    DLMF:25.6.E18
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    constraint
    n β‰₯ 1 𝑛 1 {\displaystyle{\displaystyle n\geq 1}}
    0 references
    Symbols used
    Riemann zeta function
    test
    ΞΆ ⁑ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2aqdec
    0 references
     
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