DLMF:25.11.E16 (Q7690): Difference between revisions

From testwiki
Jump to navigation Jump to search
← Older editNewer edit →
imported>Admin
imported>Admin
Property / Symbols used
 
Property / Symbols used: gamma function / rank
 
Normal rank
Property / Symbols used: gamma function / qualifier
 
test:

Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

\EulerGamma@{\NVar{z}}
Property / Symbols used: gamma function / qualifier
 
xml-id: C5.S2.E1.m2abdec

Revision as of 12:39, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:25.11.E16
No description defined

    Statements

    test
    ζ ⁡ ( 1 - s , h k ) = 2 ⁢ Γ ⁡ ( s ) ( 2 ⁢ π ⁢ k ) s ⁢ ∑ r = 1 k cos ⁡ ( π ⁢ s 2 - 2 ⁢ π ⁢ r ⁢ h k ) ⁢ ζ ⁡ ( s , r k ) , Hurwitz-zeta 1 𝑠 ℎ 𝑘 2 Euler-Gamma 𝑠 superscript 2 𝜋 𝑘 𝑠 superscript subscript 𝑟 1 𝑘 𝜋 𝑠 2 2 𝜋 𝑟 ℎ 𝑘 Hurwitz-zeta 𝑠 𝑟 𝑘 {\displaystyle{\displaystyle\zeta\left(1-s,\frac{h}{k}\right)=\frac{2\Gamma% \left(s\right)}{(2\pi k)^{s}}\*\sum_{r=1}^{k}\cos\left(\frac{\pi s}{2}-\frac{2% \pi rh}{k}\right)\zeta\left(s,\frac{r}{k}\right),}}
    0 references
    DLMF id
    DLMF:25.11.E16
    0 references
    constraint
    1 ≤ h ≤ k 1 ℎ 𝑘 {\displaystyle{\displaystyle 1\leq h\leq k}}
    0 references
    Symbols used
    gamma function
    test
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q7690&oldid=43228"