Formula:8393

Digital Library of Mathematical Functions ID 25.11.E26

${\displaystyle{\displaystyle\zeta\left(s,a\right)=-s\int_{-a}^{\infty}\frac{x-\left\lfloor x\right\rfloor-\frac{1}{2}}{(x+a)^{s+1}}\mathrm{d}x,}}$

Constraint(s)

${\displaystyle{\displaystyle-1<\Re s<0}}$
${\displaystyle{\displaystyle-1<\Re s<0}}$
${\displaystyle{\displaystyle 0<a\leq 1}}$

Symbols List

• ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$: Hurwitz zeta function
• ${\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}$: differential of x
• ${\displaystyle{\displaystyle\left\lfloor\NVar{x}\right\rfloor}}$:
• ${\displaystyle{\displaystyle\int}}$: integral
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle x}}$: real variable
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle s}}$: complex variable
 

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