DLMF:25.5.E5 (Q7618): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(One intermediate revision by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q12152 / rank
 
Normal rank
Property / Symbols used: Q12152 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q12152 / qualifier
 
xml-id: C25.S1.XMD5.m1ddec
Property / Symbols used
 
Property / Symbols used: Q12149 / rank
 
Normal rank
Property / Symbols used: Q12149 / qualifier
 
Defining formula:

s 𝑠 {\displaystyle{\displaystyle s}}

s
Property / Symbols used: Q12149 / qualifier
 
xml-id: C25.S1.XMD7.m1ddec

Latest revision as of 13:25, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:25.5.E5
No description defined

    Statements

    Defining formula
    ζ ⁡ ( s ) = - s ⁢ ∫ 0 ∞ x - ⌊ x ⌋ - 1 2 x s + 1 ⁢ d x , Riemann-zeta 𝑠 𝑠 superscript subscript 0 𝑥 𝑥 1 2 superscript 𝑥 𝑠 1 𝑥 {\displaystyle{\displaystyle\zeta\left(s\right)=-s\int_{0}^{\infty}\frac{x-% \left\lfloor x\right\rfloor-\frac{1}{2}}{x^{s+1}}\mathrm{d}x,}}
    0 references
    DLMF id
    DLMF:25.5.E5
    0 references
    constraint
    - 1 < ℜ ⁡ s < 0 1 𝑠 0 {\displaystyle{\displaystyle-1<\Re s<0}}
    0 references
    Symbols used
    Riemann zeta function
    Defining formula
    ζ ⁡ ( s ) Riemann-zeta 𝑠 {\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}
    xml-id
    C25.S2.E1.m2addec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1addec
    0 references
    Q11169
    Defining formula
    ⌊ x ⌋ 𝑥 {\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}
    xml-id
    introduction.Sx4.p1.t1.r17.m4adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3addec
    0 references
    Q10811
    Defining formula
    ℜ ⁡ absent {\displaystyle{\displaystyle\Re}}
    xml-id
    C1.S9.E2.m1addec
    0 references
    Q12152
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C25.S1.XMD5.m1ddec
    0 references
    Q12149
    Defining formula
    s 𝑠 {\displaystyle{\displaystyle s}}
    xml-id
    C25.S1.XMD7.m1ddec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7618&oldid=36349"