Formula:8385

Digital Library of Mathematical Functions ID 25.11.E18

${\displaystyle{\displaystyle\zeta'\left(0,a\right)=\ln\Gamma\left(a\right)-\tfrac{1}{2}\ln\left(2\pi\right),}}$

Constraint(s)

${\displaystyle{\displaystyle a>0}}$

Symbols List

• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$: Hurwitz zeta function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\ln\NVar{z}}}$: principal branch of logarithm function
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
 

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