Formula:8716

Digital Library of Mathematical Functions ID 27.4.E12

${\displaystyle{\displaystyle\sum_{n=1}^{\infty}\Lambda\left(n\right)n^{-s}=-\frac{\zeta'\left(s\right)}{\zeta\left(s\right)},}}$

Constraint(s)

${\displaystyle{\displaystyle\Re s>1}}$

Symbols List

• ${\displaystyle{\displaystyle\Lambda\left(\NVar{n}\right)}}$: Mangoldt’s function
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s}\right)}}$: Riemann zeta function
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle n}}$: positive integer
 

Resources that cite this formula

No records found.