DLMF:25.2.E12 (Q7607)

From DRMF
Revision as of 13:23, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:25.2.E12
No description defined

    Statements

    Defining formula
    ζ ⁡ ( s ) = ( 2 ⁢ π ) s ⁢ e - s - ( γ ⁢ s / 2 ) 2 ⁢ ( s - 1 ) ⁢ Γ ⁡ ( 1 2 ⁢ s + 1 ) ⁢ ∏ ρ ( 1 - s ρ ) ⁢ e s / ρ , Riemann-zeta 𝑠 superscript 2 𝜋 𝑠 superscript 𝑒 𝑠 𝑠 2 2 𝑠 1 Euler-Gamma 1 2 𝑠 1 subscript product 𝜌 1 𝑠 𝜌 superscript 𝑒 𝑠 𝜌 {\displaystyle{\displaystyle\zeta\left(s\right)=\frac{(2\pi)^{s}e^{-s-(\gamma s% /2)}}{2(s-1)\Gamma\left(\tfrac{1}{2}s+1\right)}\prod_{\rho}\left(1-\frac{s}{% \rho}\right)e^{s/\rho},}}
    0 references
    DLMF id
    DLMF:25.2.E12
    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.m2adec
    0 references
    Euler’s constant
    Defining formula
    γ {\displaystyle{\displaystyle\gamma}}
    xml-id
    C5.S2.E3.m2adec
    0 references
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2ajdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1jdec
    0 references
    Q12154
    Defining formula
    ρ 𝜌 {\displaystyle{\displaystyle\rho}}
    xml-id
    C25.S2.XMD1.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7607&oldid=35989"