27.8: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/27.8.E1 27.8.E1] || [[Item:Q8047|<math>\Dirichletchar[]@@{1}{k} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Dirichletchar[]@@{1}{k} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>DirichletCharacter[1, k, 1] == 1</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/27.8.E1 27.8.E1] || <math qid="Q8047">\Dirichletchar[]@@{1}{k} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Dirichletchar[]@@{1}{k} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>DirichletCharacter[1, k, 1] == 1</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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| [https://dlmf.nist.gov/27.8.E2 27.8.E2] || [[Item:Q8048|<math>\Dirichletchar[]@@{mn}{k} = \Dirichletchar[]@@{m}{k}\Dirichletchar[]@@{n}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Dirichletchar[]@@{mn}{k} = \Dirichletchar[]@@{m}{k}\Dirichletchar[]@@{n}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>DirichletCharacter[1, k, m*n] == DirichletCharacter[1, k, m]*DirichletCharacter[1, k, n]</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/27.8.E2 27.8.E2] || <math qid="Q8048">\Dirichletchar[]@@{mn}{k} = \Dirichletchar[]@@{m}{k}\Dirichletchar[]@@{n}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Dirichletchar[]@@{mn}{k} = \Dirichletchar[]@@{m}{k}\Dirichletchar[]@@{n}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>DirichletCharacter[1, k, m*n] == DirichletCharacter[1, k, m]*DirichletCharacter[1, k, n]</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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| [https://dlmf.nist.gov/27.8.E3 27.8.E3] || [[Item:Q8049|<math>\Dirichletchar[]@@{n+k}{k} = \Dirichletchar[]@@{n}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Dirichletchar[]@@{n+k}{k} = \Dirichletchar[]@@{n}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>DirichletCharacter[1, k, n + k] == DirichletCharacter[1, k, n]</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/27.8.E3 27.8.E3] || <math qid="Q8049">\Dirichletchar[]@@{n+k}{k} = \Dirichletchar[]@@{n}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Dirichletchar[]@@{n+k}{k} = \Dirichletchar[]@@{n}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>DirichletCharacter[1, k, n + k] == DirichletCharacter[1, k, n]</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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| [https://dlmf.nist.gov/27.8.E4 27.8.E4] || [[Item:Q8050|<math>\Dirichletchar[]@@{n}{k} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Dirichletchar[]@@{n}{k} = 0</syntaxhighlight> || <math>\pgcd{n > 1, k} > 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>DirichletCharacter[1, k, n] == 0</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/27.8.E4 27.8.E4] || <math qid="Q8050">\Dirichletchar[]@@{n}{k} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Dirichletchar[]@@{n}{k} = 0</syntaxhighlight> || <math>\pgcd{n > 1, k} > 1</math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>DirichletCharacter[1, k, n] == 0</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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| [https://dlmf.nist.gov/27.8.E8 27.8.E8] || [[Item:Q8054|<math>\Dirichletchar[]@@{n}{k} = \Dirichletchar[0]@@{n}{k}\Dirichletchar[1]@@{n}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Dirichletchar[]@@{n}{k} = \Dirichletchar[0]@@{n}{k}\Dirichletchar[1]@@{n}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>DirichletCharacter[1, k, n] == DirichletCharacter[0, k, n]*DirichletCharacter[1, k, n]</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/27.8.E8 27.8.E8] || <math qid="Q8054">\Dirichletchar[]@@{n}{k} = \Dirichletchar[0]@@{n}{k}\Dirichletchar[1]@@{n}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Dirichletchar[]@@{n}{k} = \Dirichletchar[0]@@{n}{k}\Dirichletchar[1]@@{n}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || <syntaxhighlight lang=mathematica>DirichletCharacter[1, k, n] == DirichletCharacter[0, k, n]*DirichletCharacter[1, k, n]</syntaxhighlight> || Missing Macro Error || Missing Macro Error || - || -
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Latest revision as of 12:06, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
27.8.E1 χ ⁡ ( 1 ) = 1 Dirichlet-character 1 𝑘 1 {\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 χ ⁡ ( m ⁢ n ) = χ ⁡ ( m ) ⁢ χ ⁡ ( n ) Dirichlet-character 𝑚 𝑛 𝑘 Dirichlet-character 𝑚 𝑘 Dirichlet-character 𝑛 𝑘 {\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 χ ⁡ ( n + k ) = χ ⁡ ( n ) Dirichlet-character 𝑛 𝑘 𝑘 Dirichlet-character 𝑛 𝑘 {\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 χ ⁡ ( n ) = 0 Dirichlet-character 𝑛 𝑘 0 {\displaystyle{\displaystyle\chi\left(n\right)=0}}
\Dirichletchar[]@@{n}{k} = 0		 ( n > 1 , k ) > 1 𝑛 1 𝑘 1 {\displaystyle{\displaystyle\left(n>1,k\right)>1}} 
Error

DirichletCharacter[1, k, n] == 0
Missing Macro Error Missing Macro Error - -
27.8.E8 χ ⁡ ( n ) = χ 0 ⁡ ( n ) ⁢ χ 1 ⁡ ( n ) Dirichlet-character 𝑛 𝑘 Dirichlet-character 0 𝑛 𝑘 Dirichlet-character 1 𝑛 𝑘 {\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 - -
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