Deprecated: $wgMWOAuthSharedUserIDs=false is deprecated, set $wgMWOAuthSharedUserIDs=true, $wgMWOAuthSharedUserSource='local' instead [Called from MediaWiki\HookContainer\HookContainer::run in /var/www/html/w/includes/HookContainer/HookContainer.php at line 135] in /var/www/html/w/includes/Debug/MWDebug.php on line 372
DLMF:27.4.E8 - MaRDI portal

DLMF:27.4.E8 (Q8712)

From MaRDI portal





No description defined
Language Label Description Also known as
English
DLMF:27.4.E8
No description defined

    Statements

    DLMF defining formula
    ∑ n = 1 ∞ | μ ⁡ ( n ) | ⁢ n - s = ζ ⁡ ( s ) ζ ⁡ ( 2 ⁢ s ) , superscript subscript 𝑛 1 Moebius-mu 𝑛 superscript 𝑛 𝑠 Riemann-zeta 𝑠 Riemann-zeta 2 𝑠 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}|\mu\left(n\right)|n^{-s}=\frac% {\zeta\left(s\right)}{\zeta\left(2s\right)},}}
    0 references
    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
    0 references
    Symbols used
    Möbius function
    DLMF defining formula
    μ ⁡ ( n ) Moebius-mu 𝑛 {\displaystyle{\displaystyle\mu\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E12.m2aadec
    0 references
    Riemann zeta function
    DLMF defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2addec
    0 references
    real part
    DLMF defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1addec
    0 references
    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1gdec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q8712&oldid=24176035"
    Powered by MediaWiki