Functions of Number Theory - 27.8 Dirichlet Characters

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
27.8.E1	${\displaystyle{\displaystyle\chi\left(1\right)=1}}$ \Dirichletchar[]@@{1}{k} = 1		Error	DirichletCharacter[1, k, 1] == 1	Missing Macro Error	Missing Macro Error	-	-
27.8.E2	${\displaystyle{\displaystyle\chi\left(mn\right)=\chi\left(m\right)\chi\left(n\right)}}$ \Dirichletchar[]@@{mn}{k} = \Dirichletchar[]@@{m}{k}\Dirichletchar[]@@{n}{k}		Error	DirichletCharacter[1, k, m*n] == DirichletCharacter[1, k, m]*DirichletCharacter[1, k, n]	Missing Macro Error	Missing Macro Error	-	-
27.8.E3	${\displaystyle{\displaystyle\chi\left(n+k\right)=\chi\left(n\right)}}$ \Dirichletchar[]@@{n+k}{k} = \Dirichletchar[]@@{n}{k}		Error	DirichletCharacter[1, k, n + k] == DirichletCharacter[1, k, n]	Missing Macro Error	Missing Macro Error	-	-
27.8.E4	${\displaystyle{\displaystyle\chi\left(n\right)=0}}$ \Dirichletchar[]@@{n}{k} = 0	${\displaystyle{\displaystyle\left(n>1,k\right)>1}}$	Error	DirichletCharacter[1, k, n] == 0	Missing Macro Error	Missing Macro Error	-	-
27.8.E8	${\displaystyle{\displaystyle\chi\left(n\right)=\chi_{0}\left(n\right)\chi_{1}\left(n\right)}}$ \Dirichletchar[]@@{n}{k} = \Dirichletchar[0]@@{n}{k}\Dirichletchar[1]@@{n}{k}		Error	DirichletCharacter[1, k, n] == DirichletCharacter[0, k, n]*DirichletCharacter[1, k, n]	Missing Macro Error	Missing Macro Error	-	-