4.28: Difference between revisions
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Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
Admin moved page Main Page to Verifying DLMF with Maple and Mathematica |
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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/4.28.E1 4.28.E1] | | | [https://dlmf.nist.gov/4.28.E1 4.28.E1] || <math qid="Q1838">\sinh@@{z} = \frac{e^{z}-e^{-z}}{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sinh@@{z} = \frac{e^{z}-e^{-z}}{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sinh(z) = (exp(z)- exp(- z))/(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sinh[z] == Divide[Exp[z]- Exp[- z],2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E2 4.28.E2] | | | [https://dlmf.nist.gov/4.28.E2 4.28.E2] || <math qid="Q1839">\cosh@@{z} = \frac{e^{z}+e^{-z}}{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosh@@{z} = \frac{e^{z}+e^{-z}}{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cosh(z) = (exp(z)+ exp(- z))/(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cosh[z] == Divide[Exp[z]+ Exp[- z],2]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E3 4.28.E3] | | | [https://dlmf.nist.gov/4.28.E3 4.28.E3] || <math qid="Q1840">\cosh@@{z}+\sinh@@{z} = e^{+ z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosh@@{z}+\sinh@@{z} = e^{+ z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cosh(z)+ sinh(z) = exp(+ z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cosh[z]+ Sinh[z] == Exp[+ z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E3 4.28.E3] | | | [https://dlmf.nist.gov/4.28.E3 4.28.E3] || <math qid="Q1840">\cosh@@{z}-\sinh@@{z} = e^{- z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cosh@@{z}-\sinh@@{z} = e^{- z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cosh(z)- sinh(z) = exp(- z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cosh[z]- Sinh[z] == Exp[- z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E4 4.28.E4] | | | [https://dlmf.nist.gov/4.28.E4 4.28.E4] || <math qid="Q1841">\tanh@@{z} = \frac{\sinh@@{z}}{\cosh@@{z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tanh@@{z} = \frac{\sinh@@{z}}{\cosh@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>tanh(z) = (sinh(z))/(cosh(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tanh[z] == Divide[Sinh[z],Cosh[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E5 4.28.E5] | | | [https://dlmf.nist.gov/4.28.E5 4.28.E5] || <math qid="Q1842">\csch@@{z} = \frac{1}{\sinh@@{z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\csch@@{z} = \frac{1}{\sinh@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>csch(z) = (1)/(sinh(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Csch[z] == Divide[1,Sinh[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E6 4.28.E6] | | | [https://dlmf.nist.gov/4.28.E6 4.28.E6] || <math qid="Q1843">\sech@@{z} = \frac{1}{\cosh@@{z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sech@@{z} = \frac{1}{\cosh@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sech(z) = (1)/(cosh(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sech[z] == Divide[1,Cosh[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E7 4.28.E7] | | | [https://dlmf.nist.gov/4.28.E7 4.28.E7] || <math qid="Q1844">\coth@@{z} = \frac{1}{\tanh@@{z}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\coth@@{z} = \frac{1}{\tanh@@{z}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>coth(z) = (1)/(tanh(z))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Coth[z] == Divide[1,Tanh[z]]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E8 4.28.E8] | | | [https://dlmf.nist.gov/4.28.E8 4.28.E8] || <math qid="Q1845">\sin@{iz} = i\sinh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sin@{iz} = i\sinh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sin(I*z) = I*sinh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sin[I*z] == I*Sinh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E9 4.28.E9] | | | [https://dlmf.nist.gov/4.28.E9 4.28.E9] || <math qid="Q1846">\cos@{iz} = \cosh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cos@{iz} = \cosh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cos(I*z) = cosh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cos[I*z] == Cosh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E10 4.28.E10] | | | [https://dlmf.nist.gov/4.28.E10 4.28.E10] || <math qid="Q1847">\tan@{iz} = i\tanh@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\tan@{iz} = i\tanh@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>tan(I*z) = I*tanh(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Tan[I*z] == I*Tanh[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E11 4.28.E11] | | | [https://dlmf.nist.gov/4.28.E11 4.28.E11] || <math qid="Q1848">\csc@{iz} = -i\csch@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\csc@{iz} = -i\csch@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>csc(I*z) = - I*csch(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Csc[I*z] == - I*Csch[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E12 4.28.E12] | | | [https://dlmf.nist.gov/4.28.E12 4.28.E12] || <math qid="Q1849">\sec@{iz} = \sech@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sec@{iz} = \sech@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sec(I*z) = sech(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sec[I*z] == Sech[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/4.28.E13 4.28.E13] | | | [https://dlmf.nist.gov/4.28.E13 4.28.E13] || <math qid="Q1850">\cot@{iz} = -i\coth@@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\cot@{iz} = -i\coth@@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>cot(I*z) = - I*coth(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Cot[I*z] == - I*Coth[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
|} | |} | ||
</div> | </div> |
Latest revision as of 11:08, 28 June 2021
DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
---|---|---|---|---|---|---|---|---|
4.28.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sinh@@{z} = \frac{e^{z}-e^{-z}}{2}}
\sinh@@{z} = \frac{e^{z}-e^{-z}}{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sinh(z) = (exp(z)- exp(- z))/(2)
|
Sinh[z] == Divide[Exp[z]- Exp[- z],2]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z} = \frac{e^{z}+e^{-z}}{2}}
\cosh@@{z} = \frac{e^{z}+e^{-z}}{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cosh(z) = (exp(z)+ exp(- z))/(2)
|
Cosh[z] == Divide[Exp[z]+ Exp[- z],2]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z}+\sinh@@{z} = e^{+ z}}
\cosh@@{z}+\sinh@@{z} = e^{+ z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cosh(z)+ sinh(z) = exp(+ z)
|
Cosh[z]+ Sinh[z] == Exp[+ z]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cosh@@{z}-\sinh@@{z} = e^{- z}}
\cosh@@{z}-\sinh@@{z} = e^{- z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cosh(z)- sinh(z) = exp(- z)
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Cosh[z]- Sinh[z] == Exp[- z]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tanh@@{z} = \frac{\sinh@@{z}}{\cosh@@{z}}}
\tanh@@{z} = \frac{\sinh@@{z}}{\cosh@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tanh(z) = (sinh(z))/(cosh(z))
|
Tanh[z] == Divide[Sinh[z],Cosh[z]]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csch@@{z} = \frac{1}{\sinh@@{z}}}
\csch@@{z} = \frac{1}{\sinh@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | csch(z) = (1)/(sinh(z))
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Csch[z] == Divide[1,Sinh[z]]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sech@@{z} = \frac{1}{\cosh@@{z}}}
\sech@@{z} = \frac{1}{\cosh@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sech(z) = (1)/(cosh(z))
|
Sech[z] == Divide[1,Cosh[z]]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \coth@@{z} = \frac{1}{\tanh@@{z}}}
\coth@@{z} = \frac{1}{\tanh@@{z}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | coth(z) = (1)/(tanh(z))
|
Coth[z] == Divide[1,Tanh[z]]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sin@{iz} = i\sinh@@{z}}
\sin@{iz} = i\sinh@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sin(I*z) = I*sinh(z)
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Sin[I*z] == I*Sinh[z]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cos@{iz} = \cosh@@{z}}
\cos@{iz} = \cosh@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cos(I*z) = cosh(z)
|
Cos[I*z] == Cosh[z]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E10 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \tan@{iz} = i\tanh@@{z}}
\tan@{iz} = i\tanh@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | tan(I*z) = I*tanh(z)
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Tan[I*z] == I*Tanh[z]
|
Successful | Successful | - | Successful [Tested: 7] |
4.28.E11 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \csc@{iz} = -i\csch@@{z}}
\csc@{iz} = -i\csch@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | csc(I*z) = - I*csch(z)
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Csc[I*z] == - I*Csch[z]
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Successful | Successful | - | Successful [Tested: 7] |
4.28.E12 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sec@{iz} = \sech@@{z}}
\sec@{iz} = \sech@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sec(I*z) = sech(z)
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Sec[I*z] == Sech[z]
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Successful | Successful | - | Successful [Tested: 7] |
4.28.E13 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \cot@{iz} = -i\coth@@{z}}
\cot@{iz} = -i\coth@@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | cot(I*z) = - I*coth(z)
|
Cot[I*z] == - I*Coth[z]
|
Successful | Successful | - | Successful [Tested: 7] |