Formula:8443

Digital Library of Mathematical Functions ID 25.15.E5

${\displaystyle{\displaystyle L\left(1-s,\chi\right)=\frac{k^{s-1}\Gamma\left(s\right)}{(2\pi)^{s}}\*{\left(e^{-\pi is/2}+\chi(-1)e^{\pi is/2}\right)}\*G(\chi)L\left(s,\overline{\chi}\right),}}$

Symbols List

• ${\displaystyle{\displaystyle L\left(\NVar{s},\NVar{\chi}\right)}}$: Dirichlet $$L$$ -function
• ${\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}$: gamma function
• ${\displaystyle{\displaystyle\pi}}$: the ratio of the circumference of a circle to its diameter
• ${\displaystyle{\displaystyle\overline{\NVar{z}}}}$: complex conjugate
• ${\displaystyle{\displaystyle\mathrm{e}}}$: base of natural logarithm
• ${\displaystyle{\displaystyle\mathrm{i}}}$: imaginary unit
• ${\displaystyle{\displaystyle k}}$: nonnegative integer
• ${\displaystyle{\displaystyle s}}$: complex variable
• ${\displaystyle{\displaystyle\chi(n)}}$: Dirichlet character
 

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