25.10: 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/25.10.E3 25.10.E3] || [[Item:Q7673|<math>Z(t) = 2\sum_{n=1}^{m}\frac{\cos@{\vartheta(t)-t\ln@@{n}}}{n^{1/2}}+R(t)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>Z(t) = 2\sum_{n=1}^{m}\frac{\cos@{\vartheta(t)-t\ln@@{n}}}{n^{1/2}}+R(t)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Z(t) = 2*sum((cos(vartheta(t)- t*ln(n)))/((n)^(1/2)), n = 1..m)+ R(t)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Z[t] == 2*Sum[Divide[Cos[\[CurlyTheta][t]- t*Log[n]],(n)^(1/2)], {n, 1, m}, GenerateConditions->None]+ R[t]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.6950521340+1.584276130*I
| [https://dlmf.nist.gov/25.10.E3 25.10.E3] || <math qid="Q7673">Z(t) = 2\sum_{n=1}^{m}\frac{\cos@{\vartheta(t)-t\ln@@{n}}}{n^{1/2}}+R(t)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>Z(t) = 2\sum_{n=1}^{m}\frac{\cos@{\vartheta(t)-t\ln@@{n}}}{n^{1/2}}+R(t)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>Z(t) = 2*sum((cos(vartheta(t)- t*ln(n)))/((n)^(1/2)), n = 1..m)+ R(t)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Z[t] == 2*Sum[Divide[Cos[\[CurlyTheta][t]- t*Log[n]],(n)^(1/2)], {n, 1, m}, GenerateConditions->None]+ R[t]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.6950521340+1.584276130*I
Test Values: {R = 1/2*3^(1/2)+1/2*I, Z = 1/2*3^(1/2)+1/2*I, t = -3/2, vartheta = 1/2*3^(1/2)+1/2*I, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.464793153+1.882475916*I
Test Values: {R = 1/2*3^(1/2)+1/2*I, Z = 1/2*3^(1/2)+1/2*I, t = -3/2, vartheta = 1/2*3^(1/2)+1/2*I, m = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.464793153+1.882475916*I
Test Values: {R = 1/2*3^(1/2)+1/2*I, Z = 1/2*3^(1/2)+1/2*I, t = -3/2, vartheta = 1/2*3^(1/2)+1/2*I, m = 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[-0.6950521348622749, 1.5842761296673835]
Test Values: {R = 1/2*3^(1/2)+1/2*I, Z = 1/2*3^(1/2)+1/2*I, t = -3/2, vartheta = 1/2*3^(1/2)+1/2*I, m = 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[-0.6950521348622749, 1.5842761296673835]

Latest revision as of 12:04, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
25.10.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle Z(t) = 2\sum_{n=1}^{m}\frac{\cos@{\vartheta(t)-t\ln@@{n}}}{n^{1/2}}+R(t)}
Z(t) = 2\sum_{n=1}^{m}\frac{\cos@{\vartheta(t)-t\ln@@{n}}}{n^{1/2}}+R(t)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
Z(t) = 2*sum((cos(vartheta(t)- t*ln(n)))/((n)^(1/2)), n = 1..m)+ R(t)
Z[t] == 2*Sum[Divide[Cos[\[CurlyTheta][t]- t*Log[n]],(n)^(1/2)], {n, 1, m}, GenerateConditions->None]+ R[t]
Failure Failure
Failed [300 / 300]
Result: -.6950521340+1.584276130*I
Test Values: {R = 1/2*3^(1/2)+1/2*I, Z = 1/2*3^(1/2)+1/2*I, t = -3/2, vartheta = 1/2*3^(1/2)+1/2*I, m = 1}

Result: -2.464793153+1.882475916*I
Test Values: {R = 1/2*3^(1/2)+1/2*I, Z = 1/2*3^(1/2)+1/2*I, t = -3/2, vartheta = 1/2*3^(1/2)+1/2*I, m = 2}

... skip entries to safe data
Failed [300 / 300]
Result: Complex[-0.6950521348622749, 1.5842761296673835]
Test Values: {Rule[m, 1], Rule[R, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϑ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

Result: Complex[-2.4647931552284597, 1.8824759153846262]
Test Values: {Rule[m, 2], Rule[R, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[t, -1.5], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ϑ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data