33.5: 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/33.5#Ex7 33.5#Ex7] | | | [https://dlmf.nist.gov/33.5#Ex7 33.5#Ex7] || <math qid="Q9523">\regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho}</syntaxhighlight> || <math>\realpart@@{((\ell+\frac{1}{2})+k+1)} > 0</math> || <syntaxhighlight lang=mathematica>CoulombF(ell, 0, rho) = (Pi*rho/2)^(1/2)* BesselJ(ell +(1)/(2), rho)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Failure || Missing Macro Error || Error || - | ||
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| [https://dlmf.nist.gov/33.5#Ex9 33.5#Ex9] | | | [https://dlmf.nist.gov/33.5#Ex9 33.5#Ex9] || <math qid="Q9525">\regCoulombF{0}@{0}{\rho} = \sin@@{\rho}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\regCoulombF{0}@{0}{\rho} = \sin@@{\rho}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>CoulombF(0, 0, rho) = sin(rho)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Successful || Missing Macro Error || - || - | ||
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| [https://dlmf.nist.gov/33.5.E6 33.5.E6] | | | [https://dlmf.nist.gov/33.5.E6 33.5.E6] || <math qid="Q9528">\frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!}</syntaxhighlight> || <math>\realpart@@{(\ell+1+\iunit\eta)} > 0</math> || <syntaxhighlight lang=mathematica>((2)^(ell)* factorial(ell))/(factorial(2*ell + 1)) = (1)/(doublefactorial(2*ell + 1))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(2)^\[ScriptL]* (\[ScriptL])!,(2*\[ScriptL]+ 1)!] == Divide[1,(2*\[ScriptL]+ 1)!!]</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 1]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Plus[Times[Power[2.0, ℓ], Factorial[ℓ], Power[Factorial[Plus[1.0, Times[2.0, ℓ]]], -1]], Times[-1.0, Power[Factorial2[Plus[1.0, Times[2.0, ℓ]]], -1]]] | ||
Test Values: {}</syntaxhighlight><br></div></div> | Test Values: {}</syntaxhighlight><br></div></div> | ||
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</div> | </div> | ||
Latest revision as of 12:13, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 33.5#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho}}
\regCoulombF{\ell}@{0}{\rho} = (\pi\rho/2)^{1/2}\BesselJ{\ell+\frac{1}{2}}@{\rho} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{((\ell+\frac{1}{2})+k+1)} > 0} | CoulombF(ell, 0, rho) = (Pi*rho/2)^(1/2)* BesselJ(ell +(1)/(2), rho)
|
Error
|
Failure | Missing Macro Error | Error | - |
| 33.5#Ex9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \regCoulombF{0}@{0}{\rho} = \sin@@{\rho}}
\regCoulombF{0}@{0}{\rho} = \sin@@{\rho} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | CoulombF(0, 0, rho) = sin(rho)
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Error
|
Successful | Missing Macro Error | - | - |
| 33.5.E6 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!}}
\frac{2^{\ell}\ell!}{(2\ell+1)!} = \frac{1}{(2\ell+1)!!} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \realpart@@{(\ell+1+\iunit\eta)} > 0} | ((2)^(ell)* factorial(ell))/(factorial(2*ell + 1)) = (1)/(doublefactorial(2*ell + 1))
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Divide[(2)^\[ScriptL]* (\[ScriptL])!,(2*\[ScriptL]+ 1)!] == Divide[1,(2*\[ScriptL]+ 1)!!]
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Failure | Failure | Error | Failed [1 / 1]
Result: Plus[Times[Power[2.0, ℓ], Factorial[ℓ], Power[Factorial[Plus[1.0, Times[2.0, ℓ]]], -1]], Times[-1.0, Power[Factorial2[Plus[1.0, Times[2.0, ℓ]]], -1]]]
Test Values: {}
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