DLMF:25.6.E14 (Q7651)

From DRMF
Revision as of 13:32, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:25.6.E14
No description defined

    Statements

    Defining formula
    ( - 1 ) k ⁢ ζ ( k ) ⁡ ( 1 - 2 ⁢ n ) = 2 ⁢ ( - 1 ) n ( 2 ⁢ π ) 2 ⁢ n ⁢ ∑ m = 0 k ∑ r = 0 m ( k m ) ⁢ ( m r ) ⁢ ℜ ⁡ ( c k - m ) ⁢ Γ ( r ) ⁡ ( 2 ⁢ n ) ⁢ ζ ( m - r ) ⁡ ( 2 ⁢ n ) , superscript 1 𝑘 Riemann-zeta 𝑘 1 2 𝑛 2 superscript 1 𝑛 superscript 2 𝜋 2 𝑛 superscript subscript 𝑚 0 𝑘 superscript subscript 𝑟 0 𝑚 binomial 𝑘 𝑚 binomial 𝑚 𝑟 superscript 𝑐 𝑘 𝑚 Euler-Gamma 𝑟 2 𝑛 Riemann-zeta 𝑚 𝑟 2 𝑛 {\displaystyle{\displaystyle(-1)^{k}{\zeta^{(k)}}\left(1-2n\right)=\frac{2(-1)% ^{n}}{(2\pi)^{2n}}\sum_{m=0}^{k}\sum_{r=0}^{m}\genfrac{(}{)}{0.0pt}{}{k}{m}% \genfrac{(}{)}{0.0pt}{}{m}{r}\Re(c^{k-m})\*{\Gamma^{(r)}}\left(2n\right){\zeta% ^{(m-r)}}\left(2n\right),}}
    0 references
    DLMF id
    DLMF:25.6.E14
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2aadec
    0 references
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2amdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7651&oldid=37341"