DLMF:25.11.E26 (Q7700): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1afdec

Revision as of 13:41, 2 January 2020

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DLMF:25.11.E26
No description defined

    Statements

    Defining formula
    ζ ⁡ ( s , a ) = - s ⁢ ∫ - a ∞ x - ⌊ x ⌋ - 1 2 ( x + a ) s + 1 ⁢ d x , Hurwitz-zeta 𝑠 𝑎 𝑠 superscript subscript 𝑎 𝑥 𝑥 1 2 superscript 𝑥 𝑎 𝑠 1 𝑥 {\displaystyle{\displaystyle\zeta\left(s,a\right)=-s\int_{-a}^{\infty}\frac{x-% \left\lfloor x\right\rfloor-\frac{1}{2}}{(x+a)^{s+1}}\mathrm{d}x,}}
    0 references
    DLMF id
    DLMF:25.11.E26
    0 references
    constraint
    - 1 < ℜ ⁡ s < 0 1 𝑠 0 {\displaystyle{\displaystyle-1<\Re s<0}}
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    - 1 < ℜ ⁡ s < 0 1 𝑠 0 {\displaystyle{\displaystyle-1<\Re s<0}}
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    0 < a ≤ 1 0 𝑎 1 {\displaystyle{\displaystyle 0<a\leq 1}}
    0 references
    Symbols used
    Hurwitz zeta function
    Defining formula
    ζ ⁡ ( s , a ) Hurwitz-zeta 𝑠 𝑎 {\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}
    xml-id
    C25.S11.E1.m2aaadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1afdec
    0 references
     
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