7.4: 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/7.4.E1 7.4.E1] | | | [https://dlmf.nist.gov/7.4.E1 7.4.E1] || <math qid="Q2335">\erf@{-z} = -\erf@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erf@{-z} = -\erf@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erf(- z) = - erf(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erf[- z] == - Erf[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/7.4.E2 7.4.E2] | | | [https://dlmf.nist.gov/7.4.E2 7.4.E2] || <math qid="Q2336">\erfc@{-z} = 2-\erfc@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\erfc@{-z} = 2-\erfc@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>erfc(- z) = 2 - erfc(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Erfc[- z] == 2 - Erfc[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/7.4.E4 7.4.E4] | | | [https://dlmf.nist.gov/7.4.E4 7.4.E4] || <math qid="Q2338">\DawsonsintF@{-z} = -\DawsonsintF@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\DawsonsintF@{-z} = -\DawsonsintF@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>dawson(- z) = - dawson(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>DawsonF[- z] == - DawsonF[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/7.4#Ex1 7.4#Ex1] | | | [https://dlmf.nist.gov/7.4#Ex1 7.4#Ex1] || <math qid="Q2339">\Fresnelcosint@{-z} = -\Fresnelcosint@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Fresnelcosint@{-z} = -\Fresnelcosint@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>FresnelC(- z) = - FresnelC(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelC[- z] == - FresnelC[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/7.4#Ex2 7.4#Ex2] | | | [https://dlmf.nist.gov/7.4#Ex2 7.4#Ex2] || <math qid="Q2340">\Fresnelsinint@{-z} = -\Fresnelsinint@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Fresnelsinint@{-z} = -\Fresnelsinint@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>FresnelS(- z) = - FresnelS(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelS[- z] == - FresnelS[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/7.4#Ex3 7.4#Ex3] | | | [https://dlmf.nist.gov/7.4#Ex3 7.4#Ex3] || <math qid="Q2341">\Fresnelcosint@{iz} = i\Fresnelcosint@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Fresnelcosint@{iz} = i\Fresnelcosint@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>FresnelC(I*z) = I*FresnelC(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelC[I*z] == I*FresnelC[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/7.4#Ex4 7.4#Ex4] | | | [https://dlmf.nist.gov/7.4#Ex4 7.4#Ex4] || <math qid="Q2342">\Fresnelsinint@{iz} = -i\Fresnelsinint@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Fresnelsinint@{iz} = -i\Fresnelsinint@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>FresnelS(I*z) = - I*FresnelS(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelS[I*z] == - I*FresnelS[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/7.4#Ex5 7.4#Ex5] | | | [https://dlmf.nist.gov/7.4#Ex5 7.4#Ex5] || <math qid="Q2343">\auxFresnelf@{iz} = (1/\sqrt{2})e^{\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}-i\auxFresnelf@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\auxFresnelf@{iz} = (1/\sqrt{2})e^{\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}-i\auxFresnelf@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Fresnelf(I*z) = (1/(sqrt(2)))*exp((1)/(4)*Pi*I -(1)/(2)*Pi*I*(z)^(2))- I*Fresnelf(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelF[I*z] == (1/(Sqrt[2]))*Exp[Divide[1,4]*Pi*I -Divide[1,2]*Pi*I*(z)^(2)]- I*FresnelF[z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/7.4#Ex6 7.4#Ex6] | | | [https://dlmf.nist.gov/7.4#Ex6 7.4#Ex6] || <math qid="Q2344">\auxFresnelg@{iz} = (1/\sqrt{2})e^{-\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}+i\auxFresnelg@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\auxFresnelg@{iz} = (1/\sqrt{2})e^{-\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}+i\auxFresnelg@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Fresnelg(I*z) = (1/(sqrt(2)))*exp(-(1)/(4)*Pi*I -(1)/(2)*Pi*I*(z)^(2))+ I*Fresnelg(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelG[I*z] == (1/(Sqrt[2]))*Exp[-Divide[1,4]*Pi*I -Divide[1,2]*Pi*I*(z)^(2)]+ I*FresnelG[z]</syntaxhighlight> || Failure || Failure || Successful [Tested: 7] || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/7.4#Ex7 7.4#Ex7] | | | [https://dlmf.nist.gov/7.4#Ex7 7.4#Ex7] || <math qid="Q2345">\auxFresnelf@{-z} = \sqrt{2}\cos@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelf@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\auxFresnelf@{-z} = \sqrt{2}\cos@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelf@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Fresnelf(- z) = sqrt(2)*cos((1)/(4)*Pi +(1)/(2)*Pi*(z)^(2))- Fresnelf(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelF[- z] == Sqrt[2]*Cos[Divide[1,4]*Pi +Divide[1,2]*Pi*(z)^(2)]- FresnelF[z]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 7] | ||
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| [https://dlmf.nist.gov/7.4#Ex8 7.4#Ex8] | | | [https://dlmf.nist.gov/7.4#Ex8 7.4#Ex8] || <math qid="Q2346">\auxFresnelg@{-z} = \sqrt{2}\sin@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelg@{z}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\auxFresnelg@{-z} = \sqrt{2}\sin@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelg@{z}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Fresnelg(- z) = sqrt(2)*sin((1)/(4)*Pi +(1)/(2)*Pi*(z)^(2))- Fresnelg(z)</syntaxhighlight> || <syntaxhighlight lang=mathematica>FresnelG[- z] == Sqrt[2]*Sin[Divide[1,4]*Pi +Divide[1,2]*Pi*(z)^(2)]- FresnelG[z]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 7] | ||
|} | |} | ||
</div> | </div> |
Latest revision as of 11:15, 28 June 2021
DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
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7.4.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erf@{-z} = -\erf@{z}}
\erf@{-z} = -\erf@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | erf(- z) = - erf(z)
|
Erf[- z] == - Erf[z]
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Successful | Successful | - | Successful [Tested: 7] |
7.4.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \erfc@{-z} = 2-\erfc@{z}}
\erfc@{-z} = 2-\erfc@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | erfc(- z) = 2 - erfc(z)
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Erfc[- z] == 2 - Erfc[z]
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Successful | Successful | - | Successful [Tested: 7] |
7.4.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \DawsonsintF@{-z} = -\DawsonsintF@{z}}
\DawsonsintF@{-z} = -\DawsonsintF@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | dawson(- z) = - dawson(z)
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DawsonF[- z] == - DawsonF[z]
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Successful | Successful | - | Successful [Tested: 7] |
7.4#Ex1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{-z} = -\Fresnelcosint@{z}}
\Fresnelcosint@{-z} = -\Fresnelcosint@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | FresnelC(- z) = - FresnelC(z)
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FresnelC[- z] == - FresnelC[z]
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Successful | Successful | - | Successful [Tested: 7] |
7.4#Ex2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{-z} = -\Fresnelsinint@{z}}
\Fresnelsinint@{-z} = -\Fresnelsinint@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | FresnelS(- z) = - FresnelS(z)
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FresnelS[- z] == - FresnelS[z]
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Successful | Successful | - | Successful [Tested: 7] |
7.4#Ex3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelcosint@{iz} = i\Fresnelcosint@{z}}
\Fresnelcosint@{iz} = i\Fresnelcosint@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | FresnelC(I*z) = I*FresnelC(z)
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FresnelC[I*z] == I*FresnelC[z]
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Successful | Successful | - | Successful [Tested: 7] |
7.4#Ex4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Fresnelsinint@{iz} = -i\Fresnelsinint@{z}}
\Fresnelsinint@{iz} = -i\Fresnelsinint@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | FresnelS(I*z) = - I*FresnelS(z)
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FresnelS[I*z] == - I*FresnelS[z]
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Successful | Successful | - | Successful [Tested: 7] |
7.4#Ex5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelf@{iz} = (1/\sqrt{2})e^{\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}-i\auxFresnelf@{z}}
\auxFresnelf@{iz} = (1/\sqrt{2})e^{\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}-i\auxFresnelf@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Fresnelf(I*z) = (1/(sqrt(2)))*exp((1)/(4)*Pi*I -(1)/(2)*Pi*I*(z)^(2))- I*Fresnelf(z)
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FresnelF[I*z] == (1/(Sqrt[2]))*Exp[Divide[1,4]*Pi*I -Divide[1,2]*Pi*I*(z)^(2)]- I*FresnelF[z]
|
Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
7.4#Ex6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{iz} = (1/\sqrt{2})e^{-\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}+i\auxFresnelg@{z}}
\auxFresnelg@{iz} = (1/\sqrt{2})e^{-\frac{1}{4}\pi i-\frac{1}{2}\pi iz^{2}}+i\auxFresnelg@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Fresnelg(I*z) = (1/(sqrt(2)))*exp(-(1)/(4)*Pi*I -(1)/(2)*Pi*I*(z)^(2))+ I*Fresnelg(z)
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FresnelG[I*z] == (1/(Sqrt[2]))*Exp[-Divide[1,4]*Pi*I -Divide[1,2]*Pi*I*(z)^(2)]+ I*FresnelG[z]
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Failure | Failure | Successful [Tested: 7] | Successful [Tested: 7] |
7.4#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelf@{-z} = \sqrt{2}\cos@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelf@{z}}
\auxFresnelf@{-z} = \sqrt{2}\cos@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelf@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Fresnelf(- z) = sqrt(2)*cos((1)/(4)*Pi +(1)/(2)*Pi*(z)^(2))- Fresnelf(z)
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FresnelF[- z] == Sqrt[2]*Cos[Divide[1,4]*Pi +Divide[1,2]*Pi*(z)^(2)]- FresnelF[z]
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Successful | Successful | - | Successful [Tested: 7] |
7.4#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \auxFresnelg@{-z} = \sqrt{2}\sin@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelg@{z}}
\auxFresnelg@{-z} = \sqrt{2}\sin@{\tfrac{1}{4}\pi+\tfrac{1}{2}\pi z^{2}}-\auxFresnelg@{z} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Fresnelg(- z) = sqrt(2)*sin((1)/(4)*Pi +(1)/(2)*Pi*(z)^(2))- Fresnelg(z)
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FresnelG[- z] == Sqrt[2]*Sin[Divide[1,4]*Pi +Divide[1,2]*Pi*(z)^(2)]- FresnelG[z]
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Successful | Failure | - | Successful [Tested: 7] |