Formula:8745

Digital Library of Mathematical Functions ID 27.8.E6

${\displaystyle{\displaystyle\sum_{r=1}^{\phi\left(k\right)}\chi_{r}\left(m\right)\overline{\chi}_{r}(n)=\begin{cases}\phi\left(k\right),&m\equiv n\pmod{k},\\ 0,&\mbox{otherwise}.\end{cases}}}$

Symbols List

• ${\displaystyle{\displaystyle\chi\left(\NVar{n}\right)}}$:
• ${\displaystyle{\displaystyle\phi\left(\NVar{n}\right)}}$: Euler’s totient
• ${\displaystyle{\displaystyle\overline{\NVar{z}}}}$: complex conjugate
• ${\displaystyle{\displaystyle\equiv}}$:
• ${\displaystyle{\displaystyle k}}$: positive integer
• ${\displaystyle{\displaystyle m}}$: positive integer
• ${\displaystyle{\displaystyle n}}$: positive integer
• ${\displaystyle{\displaystyle\chi\left(n\right)}}$:
 

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