Formula:8403

Digital Library of Mathematical Functions ID 25.11.E36

${\displaystyle{\displaystyle L\left(s,\chi\right)=\sum_{n=1}^{\infty}\frac{\chi(n)}{n^{s}}=k^{-s}\sum_{r=1}^{k-1}\chi(r)\zeta\left(s,\frac{r}{k}\right),}}$

Constraint(s)

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

Symbols List

• ${\displaystyle{\displaystyle L\left(\NVar{s},\NVar{\chi}\right)}}$: Dirichlet $$L$$ -function
• ${\displaystyle{\displaystyle\zeta\left(\NVar{s},\NVar{a}\right)}}$: Hurwitz zeta function
• ${\displaystyle{\displaystyle\Re}}$: real part
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle n}}$: nonnegative integer
• ${\displaystyle{\displaystyle s}}$: complex variable
• ${\displaystyle{\displaystyle\chi(n)}}$: Dirichlet character
 

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