18.39: 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
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/18.39.E3 18.39.E3] || [[Item:Q6062|<math>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 || - || -
| [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] || [[Item:Q6064|<math>\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
| [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 V ⁢ ( x ) = 1 2 ⁢ m ⁢ ω 2 ⁢ x 2 𝑉 𝑥 1 2 𝑚 superscript 𝜔 2 superscript 𝑥 2 {\displaystyle{\displaystyle V(x)=\tfrac{1}{2}m\omega^{2}x^{2}}}
V(x) = \tfrac{1}{2}m\omega^{2}x^{2}		 

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 η n ⁢ ( x ) = π - 1 4 ⁢ 2 - 1 2 ⁢ n ⁢ ( n ! ⁢ b ) - 1 2 ⁢ H n ⁡ ( x / b ) ⁢ e - x 2 / 2 ⁢ b 2 subscript 𝜂 𝑛 𝑥 superscript 𝜋 1 4 superscript 2 1 2 𝑛 superscript 𝑛 𝑏 1 2 Hermite-polynomial-H 𝑛 𝑥 𝑏 superscript 𝑒 superscript 𝑥 2 2 superscript 𝑏 2 {\displaystyle{\displaystyle\eta_{n}(x)=\pi^{-\frac{1}{4}}2^{-\frac{1}{2}n}(n!% \,b)^{-\frac{1}{2}}H_{n}\left(x/b\right)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}}		 

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
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