Formula:DLMF:25.15:E10

<< Formula:DLMF:25.15:E9

formula in Dirichlet L-functions

Formula:DLMF:25.16:E1 >>

Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \DirichletL@{0}{\chi} = \begin{cases} \displaystyle -\frac{1}{k} \sum_{r=1}^k r \chi(r), & \chi \neq \chi_1, \\ 0, & \chi = \chi_1. \end{cases} }}

Proof

We ask users to provide proof(s), reference(s) to proof(s), or further clarification on the proof(s) in this space.

Symbols List

& : logical and
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle L}}  : Dirichlet Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \DirichletL}} -function : http://dlmf.nist.gov/25.15#E1
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle {\displaystyle \Sigma}}  : sum : http://drmf.wmflabs.org/wiki/Definition:sum

Bibliography

Equation (10), Section 25.15 of DLMF.

URL links

We ask users to provide relevant URL links in this space.

<< Formula:DLMF:25.15:E9

formula in Dirichlet L-functions

Formula:DLMF:25.16:E1 >>