Formula:8434

Digital Library of Mathematical Functions ID 25.14.E2

${\displaystyle{\displaystyle\zeta\left(s,a\right)=\Phi\left(1,s,a\right),}}$

Constraint(s)

${\displaystyle{\displaystyle\Re s>1}}$
${\displaystyle{\displaystyle\Re s>1}}$
${\displaystyle{\displaystyle a\neq 0,-1,-2,\dots}}$

Symbols List

• ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$: Hurwitz zeta function
• ${\displaystyle{\displaystyle\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)}}$: Lerch’s transcendent
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle a}}$: real or complex parameter
• ${\displaystyle{\displaystyle s}}$: complex variable
 

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