DLMF:25.6.E20 (Q7657): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
Β 
imported>Admin
Β 
(3 intermediate revisions by the same user not shown)
Property / constraint
Β 

n β‰₯ 2 𝑛 2 {\displaystyle{\displaystyle n\geq 2}}

n\geq 2
Property / constraint: n β‰₯ 2 𝑛 2 {\displaystyle{\displaystyle n\geq 2}} / rank
Β 
Normal rank
Property / Symbols used
Β 
Property / Symbols used: Riemann zeta function / rank
Β 
Normal rank
Property / Symbols used: Riemann zeta function / qualifier
Β 
test:

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

\Riemannzeta@{\NVar{s}}
Property / Symbols used: Riemann zeta function / qualifier
Β 
xml-id: C25.S2.E1.m2asdec
Property / Symbols used
Β 
Property / Symbols used: Q12150 / rank
Β 
Normal rank
Property / Symbols used: Q12150 / qualifier
Β 
test:

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

k
Property / Symbols used: Q12150 / qualifier
Β 
xml-id: C25.S1.XMD1.m1kdec
Property / Symbols used
Β 
Property / Symbols used: Q12148 / rank
Β 
Normal rank
Property / Symbols used: Q12148 / qualifier
Β 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q12148 / qualifier
Β 
xml-id: C25.S1.XMD3.m1kdec

Latest revision as of 12:33, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:25.6.E20
No description defined

    Statements

    1 2 ⁒ ( 2 2 ⁒ n - 1 ) ⁒ ΞΆ ⁑ ( 2 ⁒ n ) = βˆ‘ k = 1 n - 1 ( 2 2 ⁒ n - 2 ⁒ k - 1 ) ⁒ ΞΆ ⁑ ( 2 ⁒ n - 2 ⁒ k ) ⁒ ΞΆ ⁑ ( 2 ⁒ k ) , 1 2 superscript 2 2 𝑛 1 Riemann-zeta 2 𝑛 superscript subscript π‘˜ 1 𝑛 1 superscript 2 2 𝑛 2 π‘˜ 1 Riemann-zeta 2 𝑛 2 π‘˜ Riemann-zeta 2 π‘˜ {\displaystyle{\displaystyle\tfrac{1}{2}(2^{2n}-1)\zeta\left(2n\right)=\sum_{k% =1}^{n-1}(2^{2n-2k}-1)\zeta\left(2n-2k\right)\zeta\left(2k\right),}}
    0 references
    0 references
    n β‰₯ 2 𝑛 2 {\displaystyle{\displaystyle n\geq 2}}
    0 references
    ΞΆ ⁑ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    C25.S2.E1.m2asdec
    0 references
    k π‘˜ {\displaystyle{\displaystyle k}}
    C25.S1.XMD1.m1kdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C25.S1.XMD3.m1kdec
    0 references