Formula:DLMF:25.15:E10

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formula in Dirichlet L-functions

Formula:DLMF:25.16:E1 >>

${\displaystyle{\displaystyle{\displaystyle L\left(0,\chi\right)=\begin{cases}\displaystyle-\frac{1}{k}\sum_{r=1}^{k}r\chi(r),&\chi\neq\chi_{1},\\ 0,&\chi=\chi_{1}.\end{cases}}}}$

Proof

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Symbols List

& : logical and
${\displaystyle{\displaystyle{\displaystyle L}}}$ : Dirichlet ${\displaystyle{\displaystyle{\displaystyle L}}}$-function : http://dlmf.nist.gov/25.15#E1
${\displaystyle{\displaystyle{\displaystyle\Sigma}}}$ : sum : http://drmf.wmflabs.org/wiki/Definition:sum

Bibliography

Equation (10), Section 25.15 of DLMF.

URL links

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formula in Dirichlet L-functions

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