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{{DISPLAYTITLE:Bernoulli and Euler Polynomials - 24.4 Basic Properties}}

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! scope="col" style="position: sticky; top: 0;" | DLMF 
! scope="col" style="position: sticky; top: 0;" | Formula 
! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/24.4.E1 24.4.E1] || <math qid="Q7414">\BernoullipolyB{n}@{x+1}-\BernoullipolyB{n}@{x} = nx^{n-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{x+1}-\BernoullipolyB{n}@{x} = nx^{n-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(n, x + 1)- bernoulli(n, x) = n*(x)^(n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, x + 1]- BernoulliB[n, x] == n*(x)^(n - 1)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E2 24.4.E2] || <math qid="Q7415">\EulerpolyE{n}@{x+1}+\EulerpolyE{n}@{x} = 2x^{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n}@{x+1}+\EulerpolyE{n}@{x} = 2x^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(n, x + 1)+ euler(n, x) = 2*(x)^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n, x + 1]+ EulerE[n, x] == 2*(x)^(n)</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E3 24.4.E3] || <math qid="Q7416">\BernoullipolyB{n}@{1-x} = (-1)^{n}\BernoullipolyB{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{1-x} = (-1)^{n}\BernoullipolyB{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(n, 1 - x) = (- 1)^(n)* bernoulli(n, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, 1 - x] == (- 1)^(n)* BernoulliB[n, x]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E4 24.4.E4] || <math qid="Q7417">\EulerpolyE{n}@{1-x} = (-1)^{n}\EulerpolyE{n}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n}@{1-x} = (-1)^{n}\EulerpolyE{n}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(n, 1 - x) = (- 1)^(n)* euler(n, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n, 1 - x] == (- 1)^(n)* EulerE[n, x]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E5 24.4.E5] || <math qid="Q7418">(-1)^{n}\BernoullipolyB{n}@{-x} = \BernoullipolyB{n}@{x}+nx^{n-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(-1)^{n}\BernoullipolyB{n}@{-x} = \BernoullipolyB{n}@{x}+nx^{n-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(- 1)^(n)* bernoulli(n, - x) = bernoulli(n, x)+ n*(x)^(n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(- 1)^(n)* BernoulliB[n, - x] == BernoulliB[n, x]+ n*(x)^(n - 1)</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E6 24.4.E6] || <math qid="Q7419">(-1)^{n+1}\EulerpolyE{n}@{-x} = \EulerpolyE{n}@{x}-2x^{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(-1)^{n+1}\EulerpolyE{n}@{-x} = \EulerpolyE{n}@{x}-2x^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(- 1)^(n + 1)* euler(n, - x) = euler(n, x)- 2*(x)^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(- 1)^(n + 1)* EulerE[n, - x] == EulerE[n, x]- 2*(x)^(n)</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E7 24.4.E7] || <math qid="Q7420">\sum_{k=1}^{m}k^{n} = \frac{\BernoullipolyB{n+1}@{m+1}-\BernoullinumberB{n+1}}{n+1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{k=1}^{m}k^{n} = \frac{\BernoullipolyB{n+1}@{m+1}-\BernoullinumberB{n+1}}{n+1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((k)^(n), k = 1..m) = (bernoulli(n + 1, m + 1)- bernoulli(n + 1))/(n + 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(k)^(n), {k, 1, m}, GenerateConditions->None] == Divide[BernoulliB[n + 1, m + 1]- BernoulliB[n + 1],n + 1]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E8 24.4.E8] || <math qid="Q7421">\sum_{k=1}^{m}(-1)^{m-k}k^{n} = \frac{\EulerpolyE{n}@{m+1}+(-1)^{m}\EulerpolyE{n}@{0}}{2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{k=1}^{m}(-1)^{m-k}k^{n} = \frac{\EulerpolyE{n}@{m+1}+(-1)^{m}\EulerpolyE{n}@{0}}{2}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((- 1)^(m - k)* (k)^(n), k = 1..m) = (euler(n, m + 1)+(- 1)^(m)* euler(n, 0))/(2)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(m - k)* (k)^(n), {k, 1, m}, GenerateConditions->None] == Divide[EulerE[n, m + 1]+(- 1)^(m)* EulerE[n, 0],2]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E9 24.4.E9] || <math qid="Q7422">\sum_{k=0}^{m-1}(a+dk)^{n} = {\frac{d^{n}}{n+1}\left(\BernoullipolyB{n+1}@{m+\frac{a}{d}}-\BernoullipolyB{n+1}@{\frac{a}{d}}\right)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{k=0}^{m-1}(a+dk)^{n} = {\frac{d^{n}}{n+1}\left(\BernoullipolyB{n+1}@{m+\frac{a}{d}}-\BernoullipolyB{n+1}@{\frac{a}{d}}\right)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((a + d*k)^(n), k = 0..m - 1) = ((d)^(n))/(n + 1)*(bernoulli(n + 1, m +(a)/(d))- bernoulli(n + 1, (a)/(d)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(a + d*k)^(n), {k, 0, m - 1}, GenerateConditions->None] == Divide[(d)^(n),n + 1]*(BernoulliB[n + 1, m +Divide[a,d]]- BernoulliB[n + 1, Divide[a,d]])</syntaxhighlight> || Failure || Failure || Successful [Tested: 300] || Successful [Tested: 300]
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| [https://dlmf.nist.gov/24.4.E10 24.4.E10] || <math qid="Q7423">\sum_{k=0}^{m-1}(-1)^{k}(a+dk)^{n} = {\frac{d^{n}}{2}\left((-1)^{m-1}\EulerpolyE{n}@{m+\frac{a}{d}}+\EulerpolyE{n}@{\frac{a}{d}}\right)}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{k=0}^{m-1}(-1)^{k}(a+dk)^{n} = {\frac{d^{n}}{2}\left((-1)^{m-1}\EulerpolyE{n}@{m+\frac{a}{d}}+\EulerpolyE{n}@{\frac{a}{d}}\right)}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum((- 1)^(k)*(a + d*k)^(n), k = 0..m - 1) = ((d)^(n))/(2)*((- 1)^(m - 1)* euler(n, m +(a)/(d))+ euler(n, (a)/(d)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[(- 1)^(k)*(a + d*k)^(n), {k, 0, m - 1}, GenerateConditions->None] == Divide[(d)^(n),2]*((- 1)^(m - 1)* EulerE[n, m +Divide[a,d]]+ EulerE[n, Divide[a,d]])</syntaxhighlight> || Failure || Failure || Successful [Tested: 300] || Successful [Tested: 300]
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| [https://dlmf.nist.gov/24.4.E12 24.4.E12] || <math qid="Q7425">\BernoullipolyB{n}@{x+h} = \sum_{k=0}^{n}{n\choose k}\BernoullipolyB{k}@{x}h^{n-k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{x+h} = \sum_{k=0}^{n}{n\choose k}\BernoullipolyB{k}@{x}h^{n-k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(n, x + h) = sum(binomial(n,k)*bernoulli(k, x)*(h)^(n - k), k = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, x + h] == Sum[Binomial[n,k]*BernoulliB[k, x]*(h)^(n - k), {k, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 90] || Successful [Tested: 90]
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| [https://dlmf.nist.gov/24.4.E13 24.4.E13] || <math qid="Q7426">\EulerpolyE{n}@{x+h} = \sum_{k=0}^{n}{n\choose k}\EulerpolyE{k}@{x}h^{n-k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n}@{x+h} = \sum_{k=0}^{n}{n\choose k}\EulerpolyE{k}@{x}h^{n-k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(n, x + h) = sum(binomial(n,k)*euler(k, x)*(h)^(n - k), k = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n, x + h] == Sum[Binomial[n,k]*EulerE[k, x]*(h)^(n - k), {k, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 90] || Successful [Tested: 90]
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| [https://dlmf.nist.gov/24.4.E14 24.4.E14] || <math qid="Q7427">\EulerpolyE{n-1}@{x} = \frac{2}{n}\sum_{k=0}^{n}{n\choose k}(1-2^{k})\BernoullinumberB{k}x^{n-k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n-1}@{x} = \frac{2}{n}\sum_{k=0}^{n}{n\choose k}(1-2^{k})\BernoullinumberB{k}x^{n-k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(n - 1, x) = (2)/(n)*sum(binomial(n,k)*(1 - (2)^(k))*bernoulli(k)*(x)^(n - k), k = 0..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n - 1, x] == Divide[2,n]*Sum[Binomial[n,k]*(1 - (2)^(k))*BernoulliB[k]*(x)^(n - k), {k, 0, n}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E15 24.4.E15] || <math qid="Q7428">\BernoullinumberB{2n} = \frac{2n}{2^{2n}(2^{2n}-1)}\sum_{k=0}^{n-1}{2n-1\choose 2k}\EulernumberE{2k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = \frac{2n}{2^{2n}(2^{2n}-1)}\sum_{k=0}^{n-1}{2n-1\choose 2k}\EulernumberE{2k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (2*n)/((2)^(2*n)*((2)^(2*n)- 1))*sum(binomial(2*n - 1,2*k)*euler(2*k), k = 0..n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == Divide[2*n,(2)^(2*n)*((2)^(2*n)- 1)]*Sum[Binomial[2*n - 1,2*k]*EulerE[2*k], {k, 0, n - 1}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 3]
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| [https://dlmf.nist.gov/24.4.E16 24.4.E16] || <math qid="Q7429">\EulernumberE{2n} = \frac{1}{2n+1}-\sum_{k=1}^{n}{2n\choose 2k-1}\frac{2^{2k}(2^{2k-1}-1)\BernoullinumberB{2k}}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulernumberE{2n} = \frac{1}{2n+1}-\sum_{k=1}^{n}{2n\choose 2k-1}\frac{2^{2k}(2^{2k-1}-1)\BernoullinumberB{2k}}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n) = (1)/(2*n + 1)- sum(binomial(2*n,2*k - 1)*((2)^(2*k)*((2)^(2*k - 1)- 1)*bernoulli(2*k))/(k), k = 1..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n] == Divide[1,2*n + 1]- Sum[Binomial[2*n,2*k - 1]*Divide[(2)^(2*k)*((2)^(2*k - 1)- 1)*BernoulliB[2*k],k], {k, 1, n}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| [https://dlmf.nist.gov/24.4.E17 24.4.E17] || <math qid="Q7430">\EulernumberE{2n} = 1-\sum_{k=1}^{n}{2n\choose 2k-1}\frac{2^{2k}(2^{2k}-1)\BernoullinumberB{2k}}{2k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulernumberE{2n} = 1-\sum_{k=1}^{n}{2n\choose 2k-1}\frac{2^{2k}(2^{2k}-1)\BernoullinumberB{2k}}{2k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n) = 1 - sum(binomial(2*n,2*k - 1)*((2)^(2*k)*((2)^(2*k)- 1)*bernoulli(2*k))/(2*k), k = 1..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n] == 1 - Sum[Binomial[2*n,2*k - 1]*Divide[(2)^(2*k)*((2)^(2*k)- 1)*BernoulliB[2*k],2*k], {k, 1, n}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Aborted || - || Skipped - Because timed out
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| [https://dlmf.nist.gov/24.4.E18 24.4.E18] || <math qid="Q7431">\BernoullipolyB{n}@{mx} = m^{n-1}\sum_{k=0}^{m-1}\BernoullipolyB{n}@{x+\frac{k}{m}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{mx} = m^{n-1}\sum_{k=0}^{m-1}\BernoullipolyB{n}@{x+\frac{k}{m}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(n, m*x) = (m)^(n - 1)* sum(bernoulli(n, x +(k)/(m)), k = 0..m - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, m*x] == (m)^(n - 1)* Sum[BernoulliB[n, x +Divide[k,m]], {k, 0, m - 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Successful || Successful [Tested: 27] || Successful [Tested: 27]
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| [https://dlmf.nist.gov/24.4.E19 24.4.E19] || <math qid="Q7432">\EulerpolyE{n}@{mx} = -\frac{2m^{n}}{n+1}\sum_{k=0}^{m-1}(-1)^{k}\BernoullipolyB{n+1}@{x+\frac{k}{m}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n}@{mx} = -\frac{2m^{n}}{n+1}\sum_{k=0}^{m-1}(-1)^{k}\BernoullipolyB{n+1}@{x+\frac{k}{m}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(n, m*x) = -(2*(m)^(n))/(n + 1)*sum((- 1)^(k)* bernoulli(n + 1, x +(k)/(m)), k = 0..m - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n, m*x] == -Divide[2*(m)^(n),n + 1]*Sum[(- 1)^(k)* BernoulliB[n + 1, x +Divide[k,m]], {k, 0, m - 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || <div class="toccolours mw-collapsible mw-collapsed">Failed [18 / 27]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.9166666666666667
Test Values: {Rule[m, 1], Rule[n, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.25
Test Values: {Rule[m, 1], Rule[n, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/24.4.E20 24.4.E20] || <math qid="Q7433">\EulerpolyE{n}@{mx} = m^{n}\sum_{k=0}^{m-1}(-1)^{k}\EulerpolyE{n}@{x+\frac{k}{m}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n}@{mx} = m^{n}\sum_{k=0}^{m-1}(-1)^{k}\EulerpolyE{n}@{x+\frac{k}{m}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(n, m*x) = (m)^(n)* sum((- 1)^(k)* euler(n, x +(k)/(m)), k = 0..m - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n, m*x] == (m)^(n)* Sum[(- 1)^(k)* EulerE[n, x +Divide[k,m]], {k, 0, m - 1}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || <div class="toccolours mw-collapsible mw-collapsed">Failed [9 / 27]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 3.5
Test Values: {Rule[m, 2], Rule[n, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 11.0
Test Values: {Rule[m, 2], Rule[n, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
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| [https://dlmf.nist.gov/24.4.E21 24.4.E21] || <math qid="Q7434">\BernoullipolyB{n}@{x} = 2^{n-1}\left(\BernoullipolyB{n}@{\tfrac{1}{2}x}+\BernoullipolyB{n}@{\tfrac{1}{2}x+\tfrac{1}{2}}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{x} = 2^{n-1}\left(\BernoullipolyB{n}@{\tfrac{1}{2}x}+\BernoullipolyB{n}@{\tfrac{1}{2}x+\tfrac{1}{2}}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(n, x) = (2)^(n - 1)*(bernoulli(n, (1)/(2)*x)+ bernoulli(n, (1)/(2)*x +(1)/(2)))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, x] == (2)^(n - 1)*(BernoulliB[n, Divide[1,2]*x]+ BernoulliB[n, Divide[1,2]*x +Divide[1,2]])</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E22 24.4.E22] || <math qid="Q7435">\EulerpolyE{n-1}@{x} = \frac{2}{n}\left(\BernoullipolyB{n}@{x}-2^{n}\BernoullipolyB{n}@{\tfrac{1}{2}x}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n-1}@{x} = \frac{2}{n}\left(\BernoullipolyB{n}@{x}-2^{n}\BernoullipolyB{n}@{\tfrac{1}{2}x}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(n - 1, x) = (2)/(n)*(bernoulli(n, x)- (2)^(n)* bernoulli(n, (1)/(2)*x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n - 1, x] == Divide[2,n]*(BernoulliB[n, x]- (2)^(n)* BernoulliB[n, Divide[1,2]*x])</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E23 24.4.E23] || <math qid="Q7436">\EulerpolyE{n-1}@{x} = \frac{2^{n}}{n}\left(\BernoullipolyB{n}@{\tfrac{1}{2}x+\tfrac{1}{2}}-\BernoullipolyB{n}@{\tfrac{1}{2}x}\right)</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n-1}@{x} = \frac{2^{n}}{n}\left(\BernoullipolyB{n}@{\tfrac{1}{2}x+\tfrac{1}{2}}-\BernoullipolyB{n}@{\tfrac{1}{2}x}\right)</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(n - 1, x) = ((2)^(n))/(n)*(bernoulli(n, (1)/(2)*x +(1)/(2))- bernoulli(n, (1)/(2)*x))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n - 1, x] == Divide[(2)^(n),n]*(BernoulliB[n, Divide[1,2]*x +Divide[1,2]]- BernoulliB[n, Divide[1,2]*x])</syntaxhighlight> || Failure || Failure || Successful [Tested: 9] || Successful [Tested: 9]
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| [https://dlmf.nist.gov/24.4.E24 24.4.E24] || <math qid="Q7437">\BernoullipolyB{n}@{mx} = m^{n}\BernoullipolyB{n}@{x}+n\sum_{k=1}^{n}\sum_{j=0}^{k-1}(-1)^{j}{n\choose k}\*\left(\sum_{r=1}^{m-1}\frac{e^{2\pi i(k-j)r/m}}{(1-e^{2\pi ir/m})^{n}}\right)(j+mx)^{n-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{mx} = m^{n}\BernoullipolyB{n}@{x}+n\sum_{k=1}^{n}\sum_{j=0}^{k-1}(-1)^{j}{n\choose k}\*\left(\sum_{r=1}^{m-1}\frac{e^{2\pi i(k-j)r/m}}{(1-e^{2\pi ir/m})^{n}}\right)(j+mx)^{n-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(n, m*x) = (m)^(n)* bernoulli(n, x)+ n*sum(sum((- 1)^(j)*binomial(n,k)*(sum((exp(2*Pi*I*(k - j)*r/m))/((1 - exp(2*Pi*I*r/m))^(n)), r = 1..m - 1))*(j + m*x)^(n - 1), j = 0..k - 1), k = 1..n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, m*x] == (m)^(n)* BernoulliB[n, x]+ n*Sum[Sum[(- 1)^(j)*Binomial[n,k]*(Sum[Divide[Exp[2*Pi*I*(k - j)*r/m],(1 - Exp[2*Pi*I*r/m])^(n)], {r, 1, m - 1}, GenerateConditions->None])*(j + m*x)^(n - 1), {j, 0, k - 1}, GenerateConditions->None], {k, 1, n}, GenerateConditions->None]</syntaxhighlight> || Aborted || Failure || Skipped - Because timed out || <div class="toccolours mw-collapsible mw-collapsed">Failed [17 / 27]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.0
Test Values: {Rule[m, 2], Rule[n, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 1.9999999999999991
Test Values: {Rule[m, 2], Rule[n, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- 
| [https://dlmf.nist.gov/24.4.E25 24.4.E25] || <math qid="Q7438">\BernoullipolyB{n}@{0} = (-1)^{n}\BernoullipolyB{n}@{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{0} = (-1)^{n}\BernoullipolyB{n}@{1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(n, 0) = (- 1)^(n)* bernoulli(n, 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, 0] == (- 1)^(n)* BernoulliB[n, 1]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E25 24.4.E25] || <math qid="Q7438">(-1)^{n}\BernoullipolyB{n}@{1} = \BernoullinumberB{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(-1)^{n}\BernoullipolyB{n}@{1} = \BernoullinumberB{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(- 1)^(n)* bernoulli(n, 1) = bernoulli(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(- 1)^(n)* BernoulliB[n, 1] == BernoulliB[n]</syntaxhighlight> || Successful || Failure || - || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E26 24.4.E26] || <math qid="Q7439">\EulerpolyE{n}@{0} = -\EulerpolyE{n}@{1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n}@{0} = -\EulerpolyE{n}@{1}</syntaxhighlight> || <math>n > 0</math> || <syntaxhighlight lang=mathematica>euler(n, 0) = - euler(n, 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n, 0] == - EulerE[n, 1]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E26 24.4.E26] || <math qid="Q7439">-\EulerpolyE{n}@{1} = -\frac{2}{n+1}(2^{n+1}-1)\BernoullinumberB{n+1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\EulerpolyE{n}@{1} = -\frac{2}{n+1}(2^{n+1}-1)\BernoullinumberB{n+1}</syntaxhighlight> || <math>n > 0</math> || <syntaxhighlight lang=mathematica>- euler(n, 1) = -(2)/(n + 1)*((2)^(n + 1)- 1)*bernoulli(n + 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- EulerE[n, 1] == -Divide[2,n + 1]*((2)^(n + 1)- 1)*BernoulliB[n + 1]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E27 24.4.E27] || <math qid="Q7440">\BernoullipolyB{n}@{\tfrac{1}{2}} = -(1-2^{1-n})\BernoullinumberB{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{\tfrac{1}{2}} = -(1-2^{1-n})\BernoullinumberB{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(n, (1)/(2)) = -(1 - (2)^(1 - n))*bernoulli(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, Divide[1,2]] == -(1 - (2)^(1 - n))*BernoulliB[n]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E28 24.4.E28] || <math qid="Q7441">\EulerpolyE{n}@{\tfrac{1}{2}} = 2^{-n}\EulernumberE{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n}@{\tfrac{1}{2}} = 2^{-n}\EulernumberE{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(n, (1)/(2)) = (2)^(- n)* euler(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n, Divide[1,2]] == (2)^(- n)* EulerE[n]</syntaxhighlight> || Missing Macro Error || Successful || - || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E29 24.4.E29] || <math qid="Q7442">\BernoullipolyB{2n}@{\tfrac{1}{3}} = \BernoullipolyB{2n}@{\tfrac{2}{3}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{2n}@{\tfrac{1}{3}} = \BernoullipolyB{2n}@{\tfrac{2}{3}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n, (1)/(3)) = bernoulli(2*n, (2)/(3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n, Divide[1,3]] == BernoulliB[2*n, Divide[2,3]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E29 24.4.E29] || <math qid="Q7442">\BernoullipolyB{2n}@{\tfrac{2}{3}} = -\tfrac{1}{2}(1-3^{1-2n})\BernoullinumberB{2n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{2n}@{\tfrac{2}{3}} = -\tfrac{1}{2}(1-3^{1-2n})\BernoullinumberB{2n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n, (2)/(3)) = -(1)/(2)*(1 - (3)^(1 - 2*n))*bernoulli(2*n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n, Divide[2,3]] == -Divide[1,2]*(1 - (3)^(1 - 2*n))*BernoulliB[2*n]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E30 24.4.E30] || <math qid="Q7443">\EulerpolyE{2n-1}@{\tfrac{1}{3}} = -\EulerpolyE{2n-1}@{\tfrac{2}{3}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{2n-1}@{\tfrac{1}{3}} = -\EulerpolyE{2n-1}@{\tfrac{2}{3}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n - 1, (1)/(3)) = - euler(2*n - 1, (2)/(3))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n - 1, Divide[1,3]] == - EulerE[2*n - 1, Divide[2,3]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 1] || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E30 24.4.E30] || <math qid="Q7443">-\EulerpolyE{2n-1}@{\tfrac{2}{3}} = -\frac{(1-3^{1-2n})(2^{2n}-1)}{2n}\BernoullinumberB{2n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>-\EulerpolyE{2n-1}@{\tfrac{2}{3}} = -\frac{(1-3^{1-2n})(2^{2n}-1)}{2n}\BernoullinumberB{2n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>- euler(2*n - 1, (2)/(3)) = -((1 - (3)^(1 - 2*n))*((2)^(2*n)- 1))/(2*n)*bernoulli(2*n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>- EulerE[2*n - 1, Divide[2,3]] == -Divide[(1 - (3)^(1 - 2*n))*((2)^(2*n)- 1),2*n]*BernoulliB[2*n]</syntaxhighlight> || Failure || Failure || Successful [Tested: 1] || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E31 24.4.E31] || <math qid="Q7444">\BernoullipolyB{n}@{\tfrac{1}{4}} = (-1)^{n}\BernoullipolyB{n}@{\tfrac{3}{4}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{\tfrac{1}{4}} = (-1)^{n}\BernoullipolyB{n}@{\tfrac{3}{4}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(n, (1)/(4)) = (- 1)^(n)* bernoulli(n, (3)/(4))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, Divide[1,4]] == (- 1)^(n)* BernoulliB[n, Divide[3,4]]</syntaxhighlight> || Failure || Successful || Successful [Tested: 1] || Successful [Tested: 1]
|- 
| [https://dlmf.nist.gov/24.4.E31 24.4.E31] || <math qid="Q7444">(-1)^{n}\BernoullipolyB{n}@{\tfrac{3}{4}} = -\frac{1-2^{1-n}}{2^{n}}\BernoullinumberB{n}-\frac{n}{4^{n}}\EulernumberE{n-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(-1)^{n}\BernoullipolyB{n}@{\tfrac{3}{4}} = -\frac{1-2^{1-n}}{2^{n}}\BernoullinumberB{n}-\frac{n}{4^{n}}\EulernumberE{n-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(- 1)^(n)* bernoulli(n, (3)/(4)) = -(1 - (2)^(1 - n))/((2)^(n))*bernoulli(n)-(n)/((4)^(n))*euler(n - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(- 1)^(n)* BernoulliB[n, Divide[3,4]] == -Divide[1 - (2)^(1 - n),(2)^(n)]*BernoulliB[n]-Divide[n,(4)^(n)]*EulerE[n - 1]</syntaxhighlight> || Missing Macro Error || Failure || Skip - symbolical successful subtest || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E32 24.4.E32] || <math qid="Q7445">\BernoullipolyB{2n}@{\tfrac{1}{6}} = \BernoullipolyB{2n}@{\tfrac{5}{6}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{2n}@{\tfrac{1}{6}} = \BernoullipolyB{2n}@{\tfrac{5}{6}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n, (1)/(6)) = bernoulli(2*n, (5)/(6))</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n, Divide[1,6]] == BernoulliB[2*n, Divide[5,6]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E32 24.4.E32] || <math qid="Q7445">\BernoullipolyB{2n}@{\tfrac{5}{6}} = \tfrac{1}{2}(1-2^{1-2n})(1-3^{1-2n})\BernoullinumberB{2n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{2n}@{\tfrac{5}{6}} = \tfrac{1}{2}(1-2^{1-2n})(1-3^{1-2n})\BernoullinumberB{2n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n, (5)/(6)) = (1)/(2)*(1 - (2)^(1 - 2*n))*(1 - (3)^(1 - 2*n))*bernoulli(2*n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n, Divide[5,6]] == Divide[1,2]*(1 - (2)^(1 - 2*n))*(1 - (3)^(1 - 2*n))*BernoulliB[2*n]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E33 24.4.E33] || <math qid="Q7446">\EulerpolyE{2n}@{\tfrac{1}{6}} = \EulerpolyE{2n}@{\tfrac{5}{6}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{2n}@{\tfrac{1}{6}} = \EulerpolyE{2n}@{\tfrac{5}{6}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n, (1)/(6)) = euler(2*n, (5)/(6))</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n, Divide[1,6]] == EulerE[2*n, Divide[5,6]]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E33 24.4.E33] || <math qid="Q7446">\EulerpolyE{2n}@{\tfrac{5}{6}} = \frac{1+3^{-2n}}{2^{2n+1}}\EulernumberE{2n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{2n}@{\tfrac{5}{6}} = \frac{1+3^{-2n}}{2^{2n+1}}\EulernumberE{2n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n, (5)/(6)) = (1 + (3)^(- 2*n))/((2)^(2*n + 1))*euler(2*n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n, Divide[5,6]] == Divide[1 + (3)^(- 2*n),(2)^(2*n + 1)]*EulerE[2*n]</syntaxhighlight> || Missing Macro Error || Failure || Skip - symbolical successful subtest || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E34 24.4.E34] || <math qid="Q7447">\deriv{}{x}\BernoullipolyB{n}@{x} = n\BernoullipolyB{n-1}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{x}\BernoullipolyB{n}@{x} = n\BernoullipolyB{n-1}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(bernoulli(n, x), x) = n*bernoulli(n - 1, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[BernoulliB[n, x], x] == n*BernoulliB[n - 1, x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E35 24.4.E35] || <math qid="Q7448">\deriv{}{x}\EulerpolyE{n}@{x} = n\EulerpolyE{n-1}@{x}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\deriv{}{x}\EulerpolyE{n}@{x} = n\EulerpolyE{n-1}@{x}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>diff(euler(n, x), x) = n*euler(n - 1, x)</syntaxhighlight> || <syntaxhighlight lang=mathematica>D[EulerE[n, x], x] == n*EulerE[n - 1, x]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 3]
|- 
| [https://dlmf.nist.gov/24.4.E37 24.4.E37] || <math qid="Q7450">\BernoullipolyB{n}@{x+h} = (B(x)+h)^{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{x+h} = (B(x)+h)^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(n, x + h) = (B(x)+ h)^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, x + h] == (B[x]+ h)^(n)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.299038106-.7500000000*I
Test Values: {B = 1/2*3^(1/2)+1/2*I, h = 1/2*3^(1/2)+1/2*I, x = 3/2, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .23717473e-1-3.546633371*I
Test Values: {B = 1/2*3^(1/2)+1/2*I, h = 1/2*3^(1/2)+1/2*I, x = 3/2, 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[-0.299038105676658, -0.7499999999999998]
Test Values: {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[0.023717474235543268, -3.546633369868303]
Test Values: {Rule[B, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/24.4.E38 24.4.E38] || <math qid="Q7451">P(E(x)+1)+P(E(x)) = 2P(x)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>P(E(x)+1)+P(E(x)) = 2P(x)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">P(E(x)+ 1)+ P(E(x)) = 2*P(x)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">P[E[x]+ 1]+ P[E[x]] == 2*P[x]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- 
| [https://dlmf.nist.gov/24.4.E39 24.4.E39] || <math qid="Q7452">\EulerpolyE{n}@{x+h} = (E(x)+h)^{n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{n}@{x+h} = (E(x)+h)^{n}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(n, x + h) = (E(x)+ h)^(n)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[n, x + h] == (E[x]+ h)^(n)</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [300 / 300]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: -.299038106-.7500000000*I
Test Values: {E = 1/2*3^(1/2)+1/2*I, h = 1/2*3^(1/2)+1/2*I, x = 3/2, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: -.142949194-3.546633371*I
Test Values: {E = 1/2*3^(1/2)+1/2*I, h = 1/2*3^(1/2)+1/2*I, x = 3/2, 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[-0.299038105676658, -0.7499999999999998]
Test Values: {Rule[E, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 1], Rule[x, 1.5]}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: Complex[-0.14294919243112325, -3.546633369868303]
Test Values: {Rule[E, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[h, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[n, 2], Rule[x, 1.5]}</syntaxhighlight><br>... skip entries to safe data</div></div>
|}
</div>