18.39: 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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| [https://dlmf.nist.gov/18.39.E3 18.39.E3] | | | [https://dlmf.nist.gov/18.39.E3 18.39.E3] || <math qid="Q6062">V(x) = \tfrac{1}{2}m\omega^{2}x^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>V(x) = \tfrac{1}{2}m\omega^{2}x^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">V(x) = (1)/(2)*m*(omega)^(2)* (x)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">V[x] == Divide[1,2]*m*\[Omega]^(2)* (x)^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || - | ||
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| [https://dlmf.nist.gov/18.39.E5 18.39.E5] | | | [https://dlmf.nist.gov/18.39.E5 18.39.E5] || <math qid="Q6064">\eta_{n}(x) = \pi^{-\frac{1}{4}}2^{-\frac{1}{2}n}(n!\,b)^{-\frac{1}{2}}\HermitepolyH{n}@{x/b}e^{-x^{2}/2b^{2}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\eta_{n}(x) = \pi^{-\frac{1}{4}}2^{-\frac{1}{2}n}(n!\,b)^{-\frac{1}{2}}\HermitepolyH{n}@{x/b}e^{-x^{2}/2b^{2}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>eta[n](x) = (Pi)^(-(1)/(4))* (2)^(-(1)/(2)*n)*(factorial(n)*b)^(-(1)/(2))* HermiteH(n, x/b)*exp(- (x)^(2)/2*(b)^(2))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[\[Eta], n][x] == (Pi)^(-Divide[1,4])* (2)^(-Divide[1,2]*n)*((n)!*b)^(-Divide[1,2])* HermiteH[n, x/b]*Exp[- (x)^(2)/2*(b)^(2)]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.299038106+.6809960435*I | ||
Test Values: {b = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, eta[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.299038106+.7845019783*I | Test Values: {b = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, eta[n] = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.299038106+.7845019783*I | ||
Test Values: {b = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, eta[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.299038105676658, 0.6809960434853285] | Test Values: {b = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, eta[n] = 1/2*3^(1/2)+1/2*I, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.299038105676658, 0.6809960434853285] | ||
Latest revision as of 11:48, 28 June 2021
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 18.39.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle V(x) = \tfrac{1}{2}m\omega^{2}x^{2}}
V(x) = \tfrac{1}{2}m\omega^{2}x^{2} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | V(x) = (1)/(2)*m*(omega)^(2)* (x)^(2) |
V[x] == Divide[1,2]*m*\[Omega]^(2)* (x)^(2) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 18.39.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta_{n}(x) = \pi^{-\frac{1}{4}}2^{-\frac{1}{2}n}(n!\,b)^{-\frac{1}{2}}\HermitepolyH{n}@{x/b}e^{-x^{2}/2b^{2}}}
\eta_{n}(x) = \pi^{-\frac{1}{4}}2^{-\frac{1}{2}n}(n!\,b)^{-\frac{1}{2}}\HermitepolyH{n}@{x/b}e^{-x^{2}/2b^{2}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | eta[n](x) = (Pi)^(-(1)/(4))* (2)^(-(1)/(2)*n)*(factorial(n)*b)^(-(1)/(2))* HermiteH(n, x/b)*exp(- (x)^(2)/2*(b)^(2))
|
Subscript[\[Eta], n][x] == (Pi)^(-Divide[1,4])* (2)^(-Divide[1,2]*n)*((n)!*b)^(-Divide[1,2])* HermiteH[n, x/b]*Exp[- (x)^(2)/2*(b)^(2)]
|
Failure | Failure | Failed [300 / 300] Result: 1.299038106+.6809960435*I
Test Values: {b = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, eta[n] = 1/2*3^(1/2)+1/2*I, n = 1}
Result: 1.299038106+.7845019783*I
Test Values: {b = -3/2, eta = 1/2*3^(1/2)+1/2*I, x = 3/2, eta[n] = 1/2*3^(1/2)+1/2*I, n = 2}
... skip entries to safe data |
Failed [300 / 300]
Result: Complex[1.299038105676658, 0.6809960434853285]
Test Values: {Rule[b, -1.5], Rule[n, 1], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[η, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: Complex[1.299038105676658, 0.7845019782573356]
Test Values: {Rule[b, -1.5], Rule[n, 2], Rule[x, 1.5], Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[Subscript[η, n], Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |