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.E7 - MaRDI portal

DLMF:27.4.E7 (Q8711)

From MaRDI portal





No description defined
Language Label Description Also known as
English
DLMF:27.4.E7
No description defined

    Statements

    DLMF defining formula
    ∑ n = 1 ∞ λ ⁡ ( n ) ⁢ n - s = ζ ⁡ ( 2 ⁢ s ) ζ ⁡ ( s ) , superscript subscript 𝑛 1 Liouville-lambda 𝑛 superscript 𝑛 𝑠 Riemann-zeta 2 𝑠 Riemann-zeta 𝑠 {\displaystyle{\displaystyle\sum_{n=1}^{\infty}\lambda\left(n\right)n^{-s}=% \frac{\zeta\left(2s\right)}{\zeta\left(s\right)},}}
    0 references
    constraint
    ℜ ⁡ s > 1 𝑠 1 {\displaystyle{\displaystyle\Re s>1}}
    0 references
    Symbols used
    Liouville’s function
    DLMF defining formula
    λ ⁡ ( n ) Liouville-lambda 𝑛 {\displaystyle{\displaystyle\lambda\left(\NVar{n}\right)}}
    xml-id
    C27.S2.E13.m2adec
    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.m2acdec
    0 references
    real part
    DLMF defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1acdec
    0 references
    positive integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C27.S1.XMD4.m1fdec
    0 references

    Identifiers

     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q8711&oldid=24176033"
    Powered by MediaWiki