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

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Property / constraint
 

m + n ≥ 1 𝑚 𝑛 1 {\displaystyle{\displaystyle m+n\geq 1}}

m+n\geq 1
Property / constraint: m + n ≥ 1 𝑚 𝑛 1 {\displaystyle{\displaystyle m+n\geq 1}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Riemann zeta function / rank
 
Normal rank
Property / Symbols used: Riemann zeta function / qualifier
 
Defining formula:

ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
 
xml-id: C25.S2.E1.m2ardec
Property / Symbols used
 
Property / Symbols used: Q12150 / rank
 
Normal rank
Property / Symbols used: Q12150 / qualifier
 
Defining formula:

k 𝑘 {\displaystyle{\displaystyle k}}

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

m 𝑚 {\displaystyle{\displaystyle m}}

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

Latest revision as of 13:32, 2 January 2020

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DLMF:25.6.E19
No description defined

    Statements

    Defining formula
    ( m + n + 3 2 ) ⁢ ζ ⁡ ( 2 ⁢ m + 2 ⁢ n + 2 ) = ( ∑ k = 1 m + ∑ k = 1 n ) ⁢ ζ ⁡ ( 2 ⁢ k ) ⁢ ζ ⁡ ( 2 ⁢ m + 2 ⁢ n + 2 - 2 ⁢ k ) , 𝑚 𝑛 3 2 Riemann-zeta 2 𝑚 2 𝑛 2 superscript subscript 𝑘 1 𝑚 superscript subscript 𝑘 1 𝑛 Riemann-zeta 2 𝑘 Riemann-zeta 2 𝑚 2 𝑛 2 2 𝑘 {\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),}}
    0 references
    DLMF id
    DLMF:25.6.E19
    0 references
    constraint
    m + n ≥ 1 𝑚 𝑛 1 {\displaystyle{\displaystyle m+n\geq 1}}
    0 references
    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2ardec
    0 references
    Q12150
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1jdec
    0 references
    Q12151
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C25.S1.XMD2.m1bdec
    0 references
    Q12148
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1jdec
    0 references
     
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