26.7: 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/26.7.E1 26.7.E1] || [[Item:Q7817|<math>\Bellnumber@{0} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{0} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BellB(0, 1) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[0] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
| [https://dlmf.nist.gov/26.7.E1 26.7.E1] || <math qid="Q7817">\Bellnumber@{0} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{0} = 1</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BellB(0, 1) = 1</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[0] == 1</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 1]
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| [https://dlmf.nist.gov/26.7.E2 26.7.E2] || [[Item:Q7818|<math>\Bellnumber@{n} = \sum_{k=0}^{n}\StirlingnumberS@{n}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{n} = \sum_{k=0}^{n}\StirlingnumberS@{n}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BellB(n, 1) = sum(Stirling2(n, k), k = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[n] == Sum[StirlingS2[n, k], {k, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
| [https://dlmf.nist.gov/26.7.E2 26.7.E2] || <math qid="Q7818">\Bellnumber@{n} = \sum_{k=0}^{n}\StirlingnumberS@{n}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{n} = \sum_{k=0}^{n}\StirlingnumberS@{n}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BellB(n, 1) = sum(Stirling2(n, k), k = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[n] == Sum[StirlingS2[n, k], {k, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 3] || Successful [Tested: 3]
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| [https://dlmf.nist.gov/26.7.E3 26.7.E3] || [[Item:Q7819|<math>\Bellnumber@{n} = \sum_{k=1}^{m}\frac{k^{n}}{k!}\sum_{j=0}^{m-k}\frac{(-1)^{j}}{j!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{n} = \sum_{k=1}^{m}\frac{k^{n}}{k!}\sum_{j=0}^{m-k}\frac{(-1)^{j}}{j!}</syntaxhighlight> || <math>m \geq n</math> || <syntaxhighlight lang=mathematica>BellB(n, 1) = sum(((k)^(n))/(factorial(k))*sum(((- 1)^(j))/(factorial(j)), j = 0..m - k), k = 1..m)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[n] == Sum[Divide[(k)^(n),(k)!]*Sum[Divide[(- 1)^(j),(j)!], {j, 0, m - k}, GenerateConditions->None], {k, 1, m}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || Successful [Tested: 6]
| [https://dlmf.nist.gov/26.7.E3 26.7.E3] || <math qid="Q7819">\Bellnumber@{n} = \sum_{k=1}^{m}\frac{k^{n}}{k!}\sum_{j=0}^{m-k}\frac{(-1)^{j}}{j!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{n} = \sum_{k=1}^{m}\frac{k^{n}}{k!}\sum_{j=0}^{m-k}\frac{(-1)^{j}}{j!}</syntaxhighlight> || <math>m \geq n</math> || <syntaxhighlight lang=mathematica>BellB(n, 1) = sum(((k)^(n))/(factorial(k))*sum(((- 1)^(j))/(factorial(j)), j = 0..m - k), k = 1..m)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[n] == Sum[Divide[(k)^(n),(k)!]*Sum[Divide[(- 1)^(j),(j)!], {j, 0, m - k}, GenerateConditions->None], {k, 1, m}, GenerateConditions->None]</syntaxhighlight> || Error || Failure || - || Successful [Tested: 6]
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| [https://dlmf.nist.gov/26.7.E4 26.7.E4] || [[Item:Q7820|<math>\Bellnumber@{n} = \expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{n} = \expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BellB(n, 1) = exp(- 1)*sum(((k)^(n))/(factorial(k)), k = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[n] == Exp[- 1]*Sum[Divide[(k)^(n),(k)!], {k, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
| [https://dlmf.nist.gov/26.7.E4 26.7.E4] || <math qid="Q7820">\Bellnumber@{n} = \expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{n} = \expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BellB(n, 1) = exp(- 1)*sum(((k)^(n))/(factorial(k)), k = 1..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[n] == Exp[- 1]*Sum[Divide[(k)^(n),(k)!], {k, 1, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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| [https://dlmf.nist.gov/26.7.E4 26.7.E4] || [[Item:Q7820|<math>\expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!} = 1+\floor{\expe^{-1}\sum_{k=1}^{2n}\frac{k^{n}}{k!}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!} = 1+\floor{\expe^{-1}\sum_{k=1}^{2n}\frac{k^{n}}{k!}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>exp(- 1)*sum(((k)^(n))/(factorial(k)), k = 1..infinity) = 1 + floor(exp(- 1)*sum(((k)^(n))/(factorial(k)), k = 1..2*n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[- 1]*Sum[Divide[(k)^(n),(k)!], {k, 1, Infinity}, GenerateConditions->None] == 1 + Floor[Exp[- 1]*Sum[Divide[(k)^(n),(k)!], {k, 1, 2*n}, GenerateConditions->None]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
| [https://dlmf.nist.gov/26.7.E4 26.7.E4] || <math qid="Q7820">\expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!} = 1+\floor{\expe^{-1}\sum_{k=1}^{2n}\frac{k^{n}}{k!}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!} = 1+\floor{\expe^{-1}\sum_{k=1}^{2n}\frac{k^{n}}{k!}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>exp(- 1)*sum(((k)^(n))/(factorial(k)), k = 1..infinity) = 1 + floor(exp(- 1)*sum(((k)^(n))/(factorial(k)), k = 1..2*n))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Exp[- 1]*Sum[Divide[(k)^(n),(k)!], {k, 1, Infinity}, GenerateConditions->None] == 1 + Floor[Exp[- 1]*Sum[Divide[(k)^(n),(k)!], {k, 1, 2*n}, GenerateConditions->None]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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| [https://dlmf.nist.gov/26.7.E5 26.7.E5] || [[Item:Q7821|<math>\sum_{n=0}^{\infty}\Bellnumber@{n}\frac{x^{n}}{n!} = \exp(\expe^{x}-1)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\Bellnumber@{n}\frac{x^{n}}{n!} = \exp(\expe^{x}-1)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(BellB(n, 1)*((x)^(n))/(factorial(n)), n = 0..infinity) = exp(exp(x)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[BellB[n]*Divide[(x)^(n),(n)!], {n, 0, Infinity}, GenerateConditions->None] == Exp[Exp[x]- 1]</syntaxhighlight> || Translation Error || Translation Error || - || -
| [https://dlmf.nist.gov/26.7.E5 26.7.E5] || <math qid="Q7821">\sum_{n=0}^{\infty}\Bellnumber@{n}\frac{x^{n}}{n!} = \exp(\expe^{x}-1)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\Bellnumber@{n}\frac{x^{n}}{n!} = \exp(\expe^{x}-1)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(BellB(n, 1)*((x)^(n))/(factorial(n)), n = 0..infinity) = exp(exp(x)- 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[BellB[n]*Divide[(x)^(n),(n)!], {n, 0, Infinity}, GenerateConditions->None] == Exp[Exp[x]- 1]</syntaxhighlight> || Translation Error || Translation Error || - || -
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| [https://dlmf.nist.gov/26.7.E6 26.7.E6] || [[Item:Q7822|<math>\Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BellB(n + 1, 1) = sum(binomial(n,k)*BellB(k, 1), k = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[n + 1] == Sum[Binomial[n,k]*BellB[k], {k, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
| [https://dlmf.nist.gov/26.7.E6 26.7.E6] || <math qid="Q7822">\Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BellB(n + 1, 1) = sum(binomial(n,k)*BellB(k, 1), k = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[n + 1] == Sum[Binomial[n,k]*BellB[k], {k, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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| [https://dlmf.nist.gov/26.7#Ex1 26.7#Ex1] || [[Item:Q7823|<math>\Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BellB(n + 1, 1) = sum(binomial(n,k)*BellB(n, 1), k = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[n + 1] == Sum[Binomial[n,k]*BellB[n], {k, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.
| [https://dlmf.nist.gov/26.7#Ex1 26.7#Ex1] || <math qid="Q7823">\Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>BellB(n + 1, 1) = sum(binomial(n,k)*BellB(n, 1), k = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BellB[n + 1] == Sum[Binomial[n,k]*BellB[n], {k, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.
Test Values: {n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -25.
Test Values: {n = 2}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -25.
Test Values: {n = 3}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.0
Test Values: {n = 3}</syntaxhighlight><br></div></div> || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -3.0
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Test Values: {Rule[n, 3]}</syntaxhighlight><br></div></div>
Test Values: {Rule[n, 3]}</syntaxhighlight><br></div></div>
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| [https://dlmf.nist.gov/26.7.E8 26.7.E8] || [[Item:Q7825|<math>N\ln@@{N} = n</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>N\ln@@{N} = n</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>N*ln(N) = n</syntaxhighlight> || <syntaxhighlight lang=mathematica>N*Log[N] == n</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.261799388+.4534498412*I
| [https://dlmf.nist.gov/26.7.E8 26.7.E8] || <math qid="Q7825">N\ln@@{N} = n</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>N\ln@@{N} = n</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>N*ln(N) = n</syntaxhighlight> || <syntaxhighlight lang=mathematica>N*Log[N] == n</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -1.261799388+.4534498412*I
Test Values: {N = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.261799388+.4534498412*I
Test Values: {N = 1/2*3^(1/2)+1/2*I, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -2.261799388+.4534498412*I
Test Values: {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 [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.2617993877991494, 0.4534498410585544]
Test Values: {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 [30 / 30]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: Complex[-1.2617993877991494, 0.4534498410585544]

Latest revision as of 12:05, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
26.7.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Bellnumber@{0} = 1}
\Bellnumber@{0} = 1		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
BellB(0, 1) = 1

BellB[0] == 1
Successful Successful - Successful [Tested: 1]
26.7.E2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Bellnumber@{n} = \sum_{k=0}^{n}\StirlingnumberS@{n}{k}}
\Bellnumber@{n} = \sum_{k=0}^{n}\StirlingnumberS@{n}{k}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
BellB(n, 1) = sum(Stirling2(n, k), k = 0..n)

BellB[n] == Sum[StirlingS2[n, k], {k, 0, n}, GenerateConditions->None]
Failure Successful Successful [Tested: 3] Successful [Tested: 3]
26.7.E3 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Bellnumber@{n} = \sum_{k=1}^{m}\frac{k^{n}}{k!}\sum_{j=0}^{m-k}\frac{(-1)^{j}}{j!}}
\Bellnumber@{n} = \sum_{k=1}^{m}\frac{k^{n}}{k!}\sum_{j=0}^{m-k}\frac{(-1)^{j}}{j!}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle m \geq n} 
BellB(n, 1) = sum(((k)^(n))/(factorial(k))*sum(((- 1)^(j))/(factorial(j)), j = 0..m - k), k = 1..m)

BellB[n] == Sum[Divide[(k)^(n),(k)!]*Sum[Divide[(- 1)^(j),(j)!], {j, 0, m - k}, GenerateConditions->None], {k, 1, m}, GenerateConditions->None]
Error Failure - Successful [Tested: 6]
26.7.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Bellnumber@{n} = \expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!}}
\Bellnumber@{n} = \expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
BellB(n, 1) = exp(- 1)*sum(((k)^(n))/(factorial(k)), k = 1..infinity)

BellB[n] == Exp[- 1]*Sum[Divide[(k)^(n),(k)!], {k, 1, Infinity}, GenerateConditions->None]
Failure Failure Successful [Tested: 3] Successful [Tested: 3]
26.7.E4 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!} = 1+\floor{\expe^{-1}\sum_{k=1}^{2n}\frac{k^{n}}{k!}}}
\expe^{-1}\sum_{k=1}^{\infty}\frac{k^{n}}{k!} = 1+\floor{\expe^{-1}\sum_{k=1}^{2n}\frac{k^{n}}{k!}}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
exp(- 1)*sum(((k)^(n))/(factorial(k)), k = 1..infinity) = 1 + floor(exp(- 1)*sum(((k)^(n))/(factorial(k)), k = 1..2*n))

Exp[- 1]*Sum[Divide[(k)^(n),(k)!], {k, 1, Infinity}, GenerateConditions->None] == 1 + Floor[Exp[- 1]*Sum[Divide[(k)^(n),(k)!], {k, 1, 2*n}, GenerateConditions->None]]
Failure Failure Successful [Tested: 3] Successful [Tested: 3]
26.7.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum_{n=0}^{\infty}\Bellnumber@{n}\frac{x^{n}}{n!} = \exp(\expe^{x}-1)}
\sum_{n=0}^{\infty}\Bellnumber@{n}\frac{x^{n}}{n!} = \exp(\expe^{x}-1)		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
sum(BellB(n, 1)*((x)^(n))/(factorial(n)), n = 0..infinity) = exp(exp(x)- 1)

Sum[BellB[n]*Divide[(x)^(n),(n)!], {n, 0, Infinity}, GenerateConditions->None] == Exp[Exp[x]- 1]
Translation Error Translation Error - -
26.7.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{k}}
\Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{k}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
BellB(n + 1, 1) = sum(binomial(n,k)*BellB(k, 1), k = 0..n)

BellB[n + 1] == Sum[Binomial[n,k]*BellB[k], {k, 0, n}, GenerateConditions->None]
Failure Failure Successful [Tested: 3] Successful [Tested: 3]
26.7#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{n}}
\Bellnumber@{n+1} = \sum_{k=0}^{n}\binom{n}{k}\Bellnumber@{n}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
BellB(n + 1, 1) = sum(binomial(n,k)*BellB(n, 1), k = 0..n)

BellB[n + 1] == Sum[Binomial[n,k]*BellB[n], {k, 0, n}, GenerateConditions->None]
Failure Failure
Failed [2 / 3]
Result: -3.
Test Values: {n = 2}


Result: -25.
Test Values: {n = 3}

Failed [2 / 3]
Result: -3.0
Test Values: {Rule[n, 2]}


Result: -25.0
Test Values: {Rule[n, 3]}

26.7.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle N\ln@@{N} = n}
N\ln@@{N} = n		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
N*ln(N) = n

N*Log[N] == n
Failure Failure
Failed [30 / 30]
Result: -1.261799388+.4534498412*I
Test Values: {N = 1/2*3^(1/2)+1/2*I, n = 1}


Result: -2.261799388+.4534498412*I
Test Values: {N = 1/2*3^(1/2)+1/2*I, n = 2}

... skip entries to safe data
Failed [30 / 30]
Result: Complex[-1.2617993877991494, 0.4534498410585544]
Test Values: {Rule[n, 1], Rule[N, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-2.261799387799149, 0.4534498410585544]
Test Values: {Rule[n, 2], Rule[N, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}

... skip entries to safe data
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