Formula:8384

Digital Library of Mathematical Functions ID 25.11.E17

${\displaystyle{\displaystyle\frac{\partial}{\partial a}\zeta\left(s,a\right)=-s\zeta\left(s+1,a\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re a>0}}$
${\displaystyle{\displaystyle s\neq 0,1}}$
${\displaystyle{\displaystyle\Re a>0}}$

Symbols List

• ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$: Hurwitz zeta function
• ${\displaystyle{\displaystyle\frac{\partial\NVar{f}}{\partial\NVar{x}}}}$: partial derivative of $$f$$ with respect to $$x$$
• ${\displaystyle{\displaystyle\partial\NVar{x}}}$: partial differential of $$x$$
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle s}}$: complex variable
 

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