33.22: 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
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| [https://dlmf.nist.gov/33.22.E3 33.22.E3] || [[Item:Q9687|<math>\deriv[2]{w}{x}+\left({\sf k}^{2}-\frac{2Z}{x}-\frac{\ell(\ell+1)}{x^{2}}\right)w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{x}+\left({\sf k}^{2}-\frac{2Z}{x}-\frac{\ell(\ell+1)}{x^{2}}\right)w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [x$(2)])+((k)^(2)-(2*Z)/(x)-(ell*(ell + 1))/((x)^(2)))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {x, 2}]+((k)^(2)-Divide[2*Z,x]-Divide[\[ScriptL]*(\[ScriptL]+ 1),(x)^(2)])*w == 0</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [297 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.5704416218017292, -1.0991449828236957]
| [https://dlmf.nist.gov/33.22.E3 33.22.E3] || <math qid="Q9687">\deriv[2]{w}{x}+\left({\sf k}^{2}-\frac{2Z}{x}-\frac{\ell(\ell+1)}{x^{2}}\right)w = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv[2]{w}{x}+\left({\sf k}^{2}-\frac{2Z}{x}-\frac{\ell(\ell+1)}{x^{2}}\right)w = 0</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(w, [x$(2)])+((k)^(2)-(2*Z)/(x)-(ell*(ell + 1))/((x)^(2)))*w = 0</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[w, {x, 2}]+((k)^(2)-Divide[2*Z,x]-Divide[\[ScriptL]*(\[ScriptL]+ 1),(x)^(2)])*w == 0</syntaxhighlight> || Failure || Failure || Error || <div class="toccolours mw-collapsible mw-collapsed">Failed [297 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-0.5704416218017292, -1.0991449828236957]
Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.110042339640732, -1.9880338717125847]
Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-2.110042339640732, -1.9880338717125847]
Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/33.22#Ex10 33.22#Ex10] || [[Item:Q9694|<math>r = -\eta\rho</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>r = -\eta\rho</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">r = - eta*rho</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">r == - \[Eta]*\[Rho]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.22#Ex10 33.22#Ex10] || <math qid="Q9694">r = -\eta\rho</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>r = -\eta\rho</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">r = - eta*rho</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">r == - \[Eta]*\[Rho]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/33.22#Ex11 33.22#Ex11] || [[Item:Q9695|<math>\epsilon = 1/\eta^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\epsilon = 1/\eta^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">epsilon = 1/(eta)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Epsilon] == 1/\[Eta]^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.22#Ex11 33.22#Ex11] || <math qid="Q9695">\epsilon = 1/\eta^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\epsilon = 1/\eta^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">epsilon = 1/(eta)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Epsilon] == 1/\[Eta]^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|-  
|-  
| [https://dlmf.nist.gov/33.22#Ex12 33.22#Ex12] || [[Item:Q9696|<math>z = 2\iunit\rho</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = 2\iunit\rho</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = 2*I*rho</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == 2*I*\[Rho]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.866025404-1.232050808*I
| [https://dlmf.nist.gov/33.22#Ex12 33.22#Ex12] || <math qid="Q9696">z = 2\iunit\rho</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>z = 2\iunit\rho</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>z = 2*I*rho</syntaxhighlight> || <syntaxhighlight lang=mathematica>z == 2*I*\[Rho]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.866025404-1.232050808*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000000-.8660254040*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .5000000000-.8660254040*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.8660254037844386, -1.2320508075688774]
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.8660254037844386, -1.2320508075688774]
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Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/33.22#Ex13 33.22#Ex13] || [[Item:Q9697|<math>\kappa = \iunit\eta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\kappa = \iunit\eta</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>kappa = I*eta</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Kappa] == I*\[Eta]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.366025404-.3660254040*I
| [https://dlmf.nist.gov/33.22#Ex13 33.22#Ex13] || <math qid="Q9697">\kappa = \iunit\eta</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\kappa = \iunit\eta</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>kappa = I*eta</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Kappa] == I*\[Eta]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.366025404-.3660254040*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.000000000-1.732050808*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.000000000-1.732050808*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.3660254037844386, -0.36602540378443876]
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[1.3660254037844386, -0.36602540378443876]
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Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/33.22#Ex14 33.22#Ex14] || [[Item:Q9698|<math>\rho = z/(2\iunit)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\rho = z/(2\iunit)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>rho = z/(2*I)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Rho] == z/(2*I)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6160254040+.9330127020*I
| [https://dlmf.nist.gov/33.22#Ex14 33.22#Ex14] || <math qid="Q9698">\rho = z/(2\iunit)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\rho = z/(2\iunit)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>rho = z/(2*I)</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Rho] == z/(2*I)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .6160254040+.9330127020*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4330127020+.2500000000*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .4330127020+.2500000000*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6160254037844387, 0.9330127018922193]
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [70 / 70]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.6160254037844387, 0.9330127018922193]
Line 40: Line 40:
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|-  
|-  
| [https://dlmf.nist.gov/33.22#Ex15 33.22#Ex15] || [[Item:Q9699|<math>\eta = \kappa/\iunit</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\eta = \kappa/\iunit</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>eta = kappa/I</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Eta] == \[Kappa]/I</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .3660254040+1.366025404*I
| [https://dlmf.nist.gov/33.22#Ex15 33.22#Ex15] || <math qid="Q9699">\eta = \kappa/\iunit</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\eta = \kappa/\iunit</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>eta = kappa/I</syntaxhighlight> || <syntaxhighlight lang=mathematica>\[Eta] == \[Kappa]/I</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .3660254040+1.366025404*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.732050808+1.000000000*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.732050808+1.000000000*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.36602540378443876, 1.3660254037844386]
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2-1/2*I*3^(1/2)}</syntaxhighlight><br>... skip entries to safe data</div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [96 / 100]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.36602540378443876, 1.3660254037844386]
Line 46: Line 46:
Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/33.22#Ex16 33.22#Ex16] || [[Item:Q9700|<math>r = \kappa z/2</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>r = \kappa z/2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">r = kappa*z/2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">r == \[Kappa]*z/2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.22#Ex16 33.22#Ex16] || <math qid="Q9700">r = \kappa z/2</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>r = \kappa z/2</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">r = kappa*z/2</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">r == \[Kappa]*z/2</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/33.22#Ex17 33.22#Ex17] || [[Item:Q9701|<math>\epsilon = -1/\kappa^{2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\epsilon = -1/\kappa^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">epsilon = - 1/(kappa)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Epsilon] == - 1/\[Kappa]^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.22#Ex17 33.22#Ex17] || <math qid="Q9701">\epsilon = -1/\kappa^{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\epsilon = -1/\kappa^{2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">epsilon = - 1/(kappa)^(2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Epsilon] == - 1/\[Kappa]^(2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/33.22#Ex18 33.22#Ex18] || [[Item:Q9702|<math>\eta = +\epsilon^{-1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\eta = +\epsilon^{-1/2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">eta = + (epsilon)^(- 1/2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Eta] == + \[Epsilon]^(- 1/2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.22#Ex18 33.22#Ex18] || <math qid="Q9702">\eta = +\epsilon^{-1/2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\eta = +\epsilon^{-1/2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">eta = + (epsilon)^(- 1/2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Eta] == + \[Epsilon]^(- 1/2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/33.22#Ex19 33.22#Ex19] || [[Item:Q9703|<math>\rho = -r/\eta</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\rho = -r/\eta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">rho = - r/eta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Rho] == - r/\[Eta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.22#Ex19 33.22#Ex19] || <math qid="Q9703">\rho = -r/\eta</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\rho = -r/\eta</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">rho = - r/eta</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Rho] == - r/\[Eta]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/33.22#Ex20 33.22#Ex20] || [[Item:Q9704|<math>\kappa = +(-\epsilon)^{-1/2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\kappa = +(-\epsilon)^{-1/2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">kappa = +(- epsilon)^(- 1/2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Kappa] == +(- \[Epsilon])^(- 1/2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.22#Ex20 33.22#Ex20] || <math qid="Q9704">\kappa = +(-\epsilon)^{-1/2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\kappa = +(-\epsilon)^{-1/2}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">kappa = +(- epsilon)^(- 1/2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">\[Kappa] == +(- \[Epsilon])^(- 1/2)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/33.22#Ex21 33.22#Ex21] || [[Item:Q9705|<math>z = 2r/\kappa</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = 2r/\kappa</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = 2*r/kappa</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == 2*r/\[Kappa]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/33.22#Ex21 33.22#Ex21] || <math qid="Q9705">z = 2r/\kappa</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z = 2r/\kappa</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z = 2*r/kappa</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">z == 2*r/\[Kappa]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|}
|}
</div>
</div>

Latest revision as of 12:14, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
33.22.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \deriv[2]{w}{x}+\left({\sf k}^{2}-\frac{2Z}{x}-\frac{\ell(\ell+1)}{x^{2}}\right)w = 0}
\deriv[2]{w}{x}+\left({\sf k}^{2}-\frac{2Z}{x}-\frac{\ell(\ell+1)}{x^{2}}\right)w = 0		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
diff(w, [x$(2)])+((k)^(2)-(2*Z)/(x)-(ell*(ell + 1))/((x)^(2)))*w = 0

D[w, {x, 2}]+((k)^(2)-Divide[2*Z,x]-Divide[\[ScriptL]*(\[ScriptL]+ 1),(x)^(2)])*w == 0
Failure Failure Error
Failed [297 / 300]
Result: Complex[-0.5704416218017292, -1.0991449828236957]
Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 1]}


Result: Complex[-2.110042339640732, -1.9880338717125847]
Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ℓ, 2]}

... skip entries to safe data
33.22#Ex10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = -\eta\rho}
r = -\eta\rho		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
r = - eta*rho
 
r == - \[Eta]*\[Rho]
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex11 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \epsilon = 1/\eta^{2}}
\epsilon = 1/\eta^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
epsilon = 1/(eta)^(2)
 
\[Epsilon] == 1/\[Eta]^(2)
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex12 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = 2\iunit\rho}
z = 2\iunit\rho		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
z = 2*I*rho

z == 2*I*\[Rho]
Failure Failure
Failed [70 / 70]
Result: 1.866025404-1.232050808*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}


Result: .5000000000-.8660254040*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [70 / 70]
Result: Complex[1.8660254037844386, -1.2320508075688774]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[2.598076211353316, 1.4999999999999996]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
33.22#Ex13 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \kappa = \iunit\eta}
\kappa = \iunit\eta		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
kappa = I*eta

\[Kappa] == I*\[Eta]
Failure Failure
Failed [96 / 100]
Result: 1.366025404-.3660254040*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I}


Result: 1.000000000-1.732050808*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2-1/2*I*3^(1/2)}

... skip entries to safe data
Failed [96 / 100]
Result: Complex[1.3660254037844386, -0.36602540378443876]
Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[1.0, -1.7320508075688772]
Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}

... skip entries to safe data
33.22#Ex14 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho = z/(2\iunit)}
\rho = z/(2\iunit)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
rho = z/(2*I)

\[Rho] == z/(2*I)
Failure Failure
Failed [70 / 70]
Result: .6160254040+.9330127020*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}


Result: .4330127020+.2500000000*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [70 / 70]
Result: Complex[0.6160254037844387, 0.9330127018922193]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-0.7499999999999998, 1.299038105676658]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
33.22#Ex15 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = \kappa/\iunit}
\eta = \kappa/\iunit		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
eta = kappa/I

\[Eta] == \[Kappa]/I
Failure Failure
Failed [96 / 100]
Result: .3660254040+1.366025404*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I}


Result: 1.732050808+1.000000000*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2-1/2*I*3^(1/2)}

... skip entries to safe data
Failed [96 / 100]
Result: Complex[0.36602540378443876, 1.3660254037844386]
Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[1.7320508075688772, 1.0]
Test Values: {Rule[η, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[κ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}

... skip entries to safe data
33.22#Ex16 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r = \kappa z/2}
r = \kappa z/2		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
r = kappa*z/2
 
r == \[Kappa]*z/2
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex17 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \epsilon = -1/\kappa^{2}}
\epsilon = -1/\kappa^{2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
epsilon = - 1/(kappa)^(2)
 
\[Epsilon] == - 1/\[Kappa]^(2)
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex18 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \eta = +\epsilon^{-1/2}}
\eta = +\epsilon^{-1/2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
eta = + (epsilon)^(- 1/2)
 
\[Eta] == + \[Epsilon]^(- 1/2)
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex19 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \rho = -r/\eta}
\rho = -r/\eta		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
rho = - r/eta
 
\[Rho] == - r/\[Eta]
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex20 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \kappa = +(-\epsilon)^{-1/2}}
\kappa = +(-\epsilon)^{-1/2}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
kappa = +(- epsilon)^(- 1/2)
 
\[Kappa] == +(- \[Epsilon])^(- 1/2)
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex21 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle z = 2r/\kappa}
z = 2r/\kappa		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
z = 2*r/kappa
 
z == 2*r/\[Kappa]
 Skipped - no semantic math Skipped - no semantic math - -
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