Formula:8408

Digital Library of Mathematical Functions ID 25.11.E41

${\displaystyle{\displaystyle\zeta\left(s,a+1\right)=\zeta\left(s\right)-s\zeta\left(s+1\right)a+O\left(a^{2}\right).}}$

Symbols List

• ${\displaystyle{\displaystyle O\left(\NVar{x}\right)}}$: order not exceeding
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$: Hurwitz zeta function
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle s}}$: complex variable
 

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