26.13: 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/26.13.E4 26.13.E4] || [[Item:Q7949|<math>d(n) = n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>d(n) = n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>d(n) = factorial(n)*sum((- 1)^(j)*(1)/(factorial(j)), j = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>d[n] == (n)!*Sum[(- 1)^(j)*Divide[1,(j)!], {j, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [29 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
| [https://dlmf.nist.gov/26.13.E4 26.13.E4] || <math qid="Q7949">d(n) = n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>d(n) = n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>d(n) = factorial(n)*sum((- 1)^(j)*(1)/(factorial(j)), j = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>d[n] == (n)!*Sum[(- 1)^(j)*Divide[1,(j)!], {j, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [29 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .8660254040+.5000000000*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7320508081+1.*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .7320508081+1.*I
Test Values: {d = 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 [29 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {d = 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 [29 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[0.8660254037844387, 0.49999999999999994]
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Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/26.13.E4 26.13.E4] || [[Item:Q7949|<math>n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!} = \floor{\frac{n!+\expe-2}{\expe}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!} = \floor{\frac{n!+\expe-2}{\expe}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>factorial(n)*sum((- 1)^(j)*(1)/(factorial(j)), j = 0..n) = floor((factorial(n)+ exp(1)- 2)/(exp(1)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(n)!*Sum[(- 1)^(j)*Divide[1,(j)!], {j, 0, n}, GenerateConditions->None] == Floor[Divide[(n)!+ E - 2,E]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .9999999999
| [https://dlmf.nist.gov/26.13.E4 26.13.E4] || <math qid="Q7949">n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!} = \floor{\frac{n!+\expe-2}{\expe}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!} = \floor{\frac{n!+\expe-2}{\expe}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>factorial(n)*sum((- 1)^(j)*(1)/(factorial(j)), j = 0..n) = floor((factorial(n)+ exp(1)- 2)/(exp(1)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>(n)!*Sum[(- 1)^(j)*Divide[1,(j)!], {j, 0, n}, GenerateConditions->None] == Floor[Divide[(n)!+ E - 2,E]]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [1 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .9999999999
Test Values: {n = 2}</syntaxhighlight><br></div></div> || Successful [Tested: 3]
Test Values: {n = 2}</syntaxhighlight><br></div></div> || Successful [Tested: 3]
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Latest revision as of 12:06, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
26.13.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle d(n) = n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!}}
d(n) = n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
d(n) = factorial(n)*sum((- 1)^(j)*(1)/(factorial(j)), j = 0..n)

d[n] == (n)!*Sum[(- 1)^(j)*Divide[1,(j)!], {j, 0, n}, GenerateConditions->None]
Failure Failure
Failed [29 / 30]
Result: .8660254040+.5000000000*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, n = 1}


Result: .7320508081+1.*I
Test Values: {d = 1/2*3^(1/2)+1/2*I, n = 2}

... skip entries to safe data
Failed [29 / 30]
Result: Complex[0.8660254037844387, 0.49999999999999994]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1]}


Result: Complex[0.7320508075688774, 0.9999999999999999]
Test Values: {Rule[d, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2]}

... skip entries to safe data
26.13.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!} = \floor{\frac{n!+\expe-2}{\expe}}}
n!\sum_{j=0}^{n}(-1)^{j}\frac{1}{j!} = \floor{\frac{n!+\expe-2}{\expe}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
factorial(n)*sum((- 1)^(j)*(1)/(factorial(j)), j = 0..n) = floor((factorial(n)+ exp(1)- 2)/(exp(1)))

(n)!*Sum[(- 1)^(j)*Divide[1,(j)!], {j, 0, n}, GenerateConditions->None] == Floor[Divide[(n)!+ E - 2,E]]
Failure Failure
Failed [1 / 3]
Result: .9999999999
Test Values: {n = 2}

Successful [Tested: 3]
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