DLMF:25.6.E19 (Q7656): Difference between revisions

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Property / constraint
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m + n β‰₯ 1 π‘š 𝑛 1 {\displaystyle{\displaystyle m+n\geq 1}}

m+n\geq 1
Property / constraint: m + n β‰₯ 1 π‘š 𝑛 1 {\displaystyle{\displaystyle m+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.m2ardec
Property / Symbols used
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Property / Symbols used: Q12150 / rank
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Normal rank
Property / Symbols used: Q12150 / qualifier
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test:

k π‘˜ {\displaystyle{\displaystyle k}}

k
Property / Symbols used: Q12150 / qualifier
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xml-id: C25.S1.XMD1.m1jdec
Property / Symbols used
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Property / Symbols used: Q12151 / rank
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Normal rank
Property / Symbols used: Q12151 / qualifier
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test:

m π‘š {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12151 / qualifier
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xml-id: C25.S1.XMD2.m1bdec
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.m1jdec

Latest revision as of 12:32, 2 January 2020

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DLMF:25.6.E19
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    Statements

    ( m + n + 3 2 ) ⁒ ΞΆ ⁑ ( 2 ⁒ m + 2 ⁒ n + 2 ) = ( βˆ‘ k = 1 m + βˆ‘ k = 1 n ) ⁒ ΞΆ ⁑ ( 2 ⁒ k ) ⁒ ΞΆ ⁑ ( 2 ⁒ m + 2 ⁒ n + 2 - 2 ⁒ k ) , π‘š 𝑛 3 2 Riemann-zeta 2 π‘š 2 𝑛 2 superscript subscript π‘˜ 1 π‘š superscript subscript π‘˜ 1 𝑛 Riemann-zeta 2 π‘˜ Riemann-zeta 2 π‘š 2 𝑛 2 2 π‘˜ {\displaystyle{\displaystyle\left(m+n+\tfrac{3}{2}\right)\zeta\left(2m+2n+2% \right)=\left(\sum_{k=1}^{m}+\sum_{k=1}^{n}\right)\zeta\left(2k\right)\zeta% \left(2m+2n+2-2k\right),}}
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    m + n β‰₯ 1 π‘š 𝑛 1 {\displaystyle{\displaystyle m+n\geq 1}}
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    ΞΆ ⁑ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    C25.S2.E1.m2ardec
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    k π‘˜ {\displaystyle{\displaystyle k}}
    C25.S1.XMD1.m1jdec
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    m π‘š {\displaystyle{\displaystyle m}}
    C25.S1.XMD2.m1bdec
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    n 𝑛 {\displaystyle{\displaystyle n}}
    C25.S1.XMD3.m1jdec
    0 references