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:25.11.E15 - MaRDI portal

DLMF:25.11.E15 (Q8382)

From MaRDI portal
No description defined
Language Label Description Also known as
English
DLMF:25.11.E15
No description defined

    Statements

    DLMF defining formula
    ζ ⁡ ( s , k ⁢ a ) = k - s ⁢ ∑ n = 0 k - 1 ζ ⁡ ( s , a + n k ) , Hurwitz-zeta 𝑠 𝑘 𝑎 superscript 𝑘 𝑠 superscript subscript 𝑛 0 𝑘 1 Hurwitz-zeta 𝑠 𝑎 𝑛 𝑘 {\displaystyle{\displaystyle\zeta\left(s,ka\right)=k^{-s}\*\sum_{n=0}^{k-1}% \zeta\left(s,a+\frac{n}{k}\right),}}
    0 references
    constraint
    k = 1 , 2 , 3 , … 𝑘 1 2 3 … {\displaystyle{\displaystyle k=1,2,3,\dots}}
    0 references
    Symbols used
    Hurwitz zeta function
    DLMF defining formula
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2apdec
    0 references
    nonnegative integer
    DLMF defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C25.S1.XMD1.m1adec
    0 references
    nonnegative integer
    DLMF defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C25.S1.XMD2.m1adec
    0 references
    nonnegative integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C25.S1.XMD3.m1jdec
    0 references
    real or complex parameter
    DLMF defining formula
    a 𝑎 {\displaystyle{\displaystyle a}}
    xml-id
    C25.S1.XMD6.m1ndec
    0 references
    complex variable
    DLMF defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1kdec
    0 references
     
    Retrieved from "https://portal.mardi4nfdi.de/w/index.php?title=Item:Q8382&oldid=24176447"
    Powered by MediaWiki