24.7: Difference between revisions

Latest revision as of 12:02, 28 June 2021

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
24.7.E1	${\displaystyle{\displaystyle B_{2n}=(-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{% \infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\mathrm{d}t}}$ `\BernoullinumberB{2n} = (-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\diff{t}`		bernoulli(2n) = (- 1)^(n + 1)(4n)/(1 - (2)^(1 - 2n))int(((t)^(2n - 1))/(exp(2Pit)+ 1), t = 0..infinity)	BernoulliB[2n] == (- 1)^(n + 1)Divide[4n,1 - (2)^(1 - 2n)]Integrate[Divide[(t)^(2n - 1),Exp[2Pit]+ 1], {t, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
24.7.E1	${\displaystyle{\displaystyle(-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}% \frac{t^{2n-1}}{e^{2\pi t}+1}\mathrm{d}t=(-1)^{n+1}\frac{2n}{1-2^{1-2n}}\int_{% 0}^{\infty}t^{2n-1}e^{-\pi t}\operatorname{sech}\left(\pi t\right)\mathrm{d}t}}$ `(-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\diff{t} = (-1)^{n+1}\frac{2n}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\sech@{\pi t}\diff{t}`		(- 1)^(n + 1)(4n)/(1 - (2)^(1 - 2n))int(((t)^(2n - 1))/(exp(2Pit)+ 1), t = 0..infinity) = (- 1)^(n + 1)(2n)/(1 - (2)^(1 - 2n))int((t)^(2n - 1)* exp(- Pit)sech(Pi*t), t = 0..infinity)	(- 1)^(n + 1)Divide[4n,1 - (2)^(1 - 2n)]Integrate[Divide[(t)^(2n - 1),Exp[2Pit]+ 1], {t, 0, Infinity}, GenerateConditions->None] == (- 1)^(n + 1)Divide[2n,1 - (2)^(1 - 2n)]Integrate[(t)^(2n - 1)* Exp[- Pit]Sech[Pi*t], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 3]
24.7.E2	${\displaystyle{\displaystyle B_{2n}=(-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1% }}{e^{2\pi t}-1}\mathrm{d}t}}$ `\BernoullinumberB{2n} = (-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}-1}\diff{t}`		bernoulli(2n) = (- 1)^(n + 1) 4nint(((t)^(2n - 1))/(exp(2Pi*t)- 1), t = 0..infinity)	BernoulliB[2n] == (- 1)^(n + 1) 4nIntegrate[Divide[(t)^(2n - 1),Exp[2Pi*t]- 1], {t, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
24.7.E2	${\displaystyle{\displaystyle(-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2% \pi t}-1}\mathrm{d}t=(-1)^{n+1}2n\int_{0}^{\infty}t^{2n-1}e^{-\pi t}% \operatorname{csch}\left(\pi t\right)\mathrm{d}t}}$ `(-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}-1}\diff{t} = (-1)^{n+1}2n\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\csch@{\pi t}\diff{t}`		(- 1)^(n + 1)* 4nint(((t)^(2n - 1))/(exp(2Pit)- 1), t = 0..infinity) = (- 1)^(n + 1) 2nint((t)^(2n - 1) exp(- Pit)csch(Pi*t), t = 0..infinity)	(- 1)^(n + 1)* 4nIntegrate[Divide[(t)^(2n - 1),Exp[2Pit]- 1], {t, 0, Infinity}, GenerateConditions->None] == (- 1)^(n + 1) 2nIntegrate[(t)^(2n - 1) Exp[- Pit]Csch[Pi*t], {t, 0, Infinity}, GenerateConditions->None]	Successful	Successful	Skip - symbolical successful subtest	Successful [Tested: 3]
24.7.E3	${\displaystyle{\displaystyle B_{2n}=(-1)^{n+1}\frac{\pi}{1-2^{1-2n}}\int_{0}^{% \infty}t^{2n}{\operatorname{sech}^{2}}\left(\pi t\right)\mathrm{d}t}}$ `\BernoullinumberB{2n} = (-1)^{n+1}\frac{\pi}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n}\sech^{2}@{\pi t}\diff{t}`		bernoulli(2n) = (- 1)^(n + 1)(Pi)/(1 - (2)^(1 - 2n))int((t)^(2n) (sech(Pi*t))^(2), t = 0..infinity)	BernoulliB[2n] == (- 1)^(n + 1)Divide[Pi,1 - (2)^(1 - 2n)]Integrate[(t)^(2n) (Sech[Pi*t])^(2), {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Successful [Tested: 3]	Skipped - Because timed out
24.7.E4	${\displaystyle{\displaystyle B_{2n}=(-1)^{n+1}\pi\int_{0}^{\infty}t^{2n}{% \operatorname{csch}^{2}}\left(\pi t\right)\mathrm{d}t}}$ `\BernoullinumberB{2n} = (-1)^{n+1}\pi\int_{0}^{\infty}t^{2n}\csch^{2}@{\pi t}\diff{t}`		bernoulli(2n) = (- 1)^(n + 1) Piint((t)^(2n)* (csch(Pi*t))^(2), t = 0..infinity)	BernoulliB[2n] == (- 1)^(n + 1) PiIntegrate[(t)^(2n)* (Csch[Pi*t])^(2), {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Successful [Tested: 3]	Skipped - Because timed out
24.7.E5	${\displaystyle{\displaystyle B_{2n}=(-1)^{n}\frac{2n(2n-1)}{\pi}\\int_{0}^{% \infty}t^{2n-2}\ln\left(1-e^{-2\pi t}\right)\mathrm{d}t}}$ `\BernoullinumberB{2n} = (-1)^{n}\frac{2n(2n-1)}{\pi}\\int_{0}^{\infty}t^{2n-2}\ln@{1-e^{-2\pi t}}\diff{t}`		bernoulli(2n) = (- 1)^(n)(2n(2n - 1))/(Pi) int((t)^(2n - 2) ln(1 - exp(- 2Pit)), t = 0..infinity)	BernoulliB[2n] == (- 1)^(n)Divide[2n(2n - 1),Pi] Integrate[(t)^(2n - 2) Log[1 - Exp[- 2Pit]], {t, 0, Infinity}, GenerateConditions->None]	Failure	Failure	Successful [Tested: 3]	Successful [Tested: 3]
24.7.E6	${\displaystyle{\displaystyle E_{2n}=(-1)^{n}2^{2n+1}\int_{0}^{\infty}t^{2n}% \operatorname{sech}\left(\pi t\right)\mathrm{d}t}}$ `\EulernumberE{2n} = (-1)^{n}2^{2n+1}\int_{0}^{\infty}t^{2n}\sech@{\pi t}\diff{t}`		euler(2n) = (- 1)^(n) (2)^(2n + 1) int((t)^(2n) sech(Pi*t), t = 0..infinity)	EulerE[2n] == (- 1)^(n) (2)^(2n + 1) Integrate[(t)^(2n) Sech[Pi*t], {t, 0, Infinity}, GenerateConditions->None]	Missing Macro Error	Failure	-	Successful [Tested: 3]
24.7.E7	${\displaystyle{\displaystyle B_{2n}\left(x\right)=(-1)^{n+1}2n\\int_{0}^{% \infty}\frac{\cos\left(2\pi x\right)-e^{-2\pi t}}{\cosh\left(2\pi t\right)-% \cos\left(2\pi x\right)}t^{2n-1}\mathrm{d}t}}$ `\BernoullipolyB{2n}@{x} = (-1)^{n+1}2n\\int_{0}^{\infty}\frac{\cos@{2\pi x}-e^{-2\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n-1}\diff{t}`		bernoulli(2n, x) = (- 1)^(n + 1) 2n int((cos(2Pix)- exp(- 2Pit))/(cosh(2Pit)- cos(2Pix))(t)^(2n - 1), t = 0..infinity)	BernoulliB[2n, x] == (- 1)^(n + 1) 2n Integrate[Divide[Cos[2Pix]- Exp[- 2Pit],Cosh[2Pit]- Cos[2Pix]](t)^(2n - 1), {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Failed [2 / 3] Result: .1875000000 Test Values: {x = 3/2, n = 3} Result: 6.000000000 Test Values: {x = 2, n = 3}	Skipped - Because timed out
24.7.E8	${\displaystyle{\displaystyle B_{2n+1}\left(x\right)=(-1)^{n+1}(2n+1)\\int_{0}% ^{\infty}\frac{\sin\left(2\pi x\right)}{\cosh\left(2\pi t\right)-\cos\left(2% \pi x\right)}t^{2n}\mathrm{d}t}}$ `\BernoullipolyB{2n+1}@{x} = (-1)^{n+1}(2n+1)\\int_{0}^{\infty}\frac{\sin@{2\pi x}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n}\diff{t}`		bernoulli(2n + 1, x) = (- 1)^(n + 1)(2n + 1) int((sin(2Pix))/(cosh(2Pit)- cos(2Pix))(t)^(2n), t = 0..infinity)	BernoulliB[2n + 1, x] == (- 1)^(n + 1)(2n + 1) Integrate[Divide[Sin[2Pix],Cosh[2Pit]- Cos[2Pix]](t)^(2n), {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Failed [6 / 9] Result: .7500000000 Test Values: {x = 3/2, n = 1} Result: .3125000000 Test Values: {x = 3/2, n = 2} ... skip entries to safe data	Skipped - Because timed out
24.7.E9	${\displaystyle{\displaystyle E_{2n}\left(x\right)=(-1)^{n}4\int_{0}^{\infty}% \frac{\sin\left(\pi x\right)\cosh\left(\pi t\right)}{\cosh\left(2\pi t\right)-% \cos\left(2\pi x\right)}t^{2n}\mathrm{d}t}}$ `\EulerpolyE{2n}@{x} = (-1)^{n}4\int_{0}^{\infty}\frac{\sin@{\pi x}\cosh@{\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n}\diff{t}`		euler(2n, x) = (- 1)^(n) 4int((sin(Pix)cosh(Pit))/(cosh(2Pit)- cos(2Pix))(t)^(2n), t = 0..infinity)	EulerE[2n, x] == (- 1)^(n) 4Integrate[Divide[Sin[Pix]Cosh[Pit],Cosh[2Pit]- Cos[2Pix]](t)^(2n), {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Failed [6 / 9] Result: .5000000001 Test Values: {x = 3/2, n = 1} Result: .1249999998 Test Values: {x = 3/2, n = 2} ... skip entries to safe data	Skipped - Because timed out
24.7.E10	${\displaystyle{\displaystyle E_{2n+1}\left(x\right)=(-1)^{n+1}4\\int_{0}^{% \infty}\frac{\cos\left(\pi x\right)\sinh\left(\pi t\right)}{\cosh\left(2\pi t% \right)-\cos\left(2\pi x\right)}t^{2n+1}\mathrm{d}t}}$ `\EulerpolyE{2n+1}@{x} = (-1)^{n+1}4\\int_{0}^{\infty}\frac{\cos@{\pi x}\sinh@{\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n+1}\diff{t}`		euler(2n + 1, x) = (- 1)^(n + 1) 4 * int((cos(Pix)sinh(Pit))/(cosh(2Pit)- cos(2Pix))(t)^(2*n + 1), t = 0..infinity)	EulerE[2n + 1, x] == (- 1)^(n + 1) 4 * Integrate[Divide[Cos[Pix]Sinh[Pit],Cosh[2Pit]- Cos[2Pix]](t)^(2*n + 1), {t, 0, Infinity}, GenerateConditions->None]	Failure	Aborted	Failed [6 / 9] Result: .2499999999 Test Values: {x = 3/2, n = 1} Result: .6250000031e-1 Test Values: {x = 3/2, n = 2} ... skip entries to safe data	Skipped - Because timed out
24.7.E11	${\displaystyle{\displaystyle B_{n}\left(x\right)=\frac{1}{2\pi i}\int_{-c-i% \infty}^{-c+i\infty}(x+t)^{n}\left(\frac{\pi}{\sin\left(\pi t\right)}\right)^{% 2}\mathrm{d}t}}$ `\BernoullipolyB{n}@{x} = \frac{1}{2\pi i}\int_{-c-i\infty}^{-c+i\infty}(x+t)^{n}\left(\frac{\pi}{\sin@{\pi t}}\right)^{2}\diff{t}`	${\displaystyle{\displaystyle 0<c,c<1}}$	bernoulli(n, x) = (1)/(2PiI)int((x + t)^(n)((Pi)/(sin(Pit)))^(2), t = - c - Iinfinity..- c + I*infinity)	BernoulliB[n, x] == Divide[1,2PiI]Integrate[(x + t)^(n)(Divide[Pi,Sin[Pit]])^(2), {t, - c - IInfinity, - c + I*Infinity}, GenerateConditions->None]	Failure	Failure	Failed [7 / 9] Result: 1. Test Values: {c = 1/2, x = 3/2, n = 1} Result: .9166666667 Test Values: {c = 1/2, x = 3/2, n = 2} ... skip entries to safe data	Skipped - Because timed out

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 ! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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-| [https://dlmf.nist.gov/24.7.E1 24.7.E1] || [[Item:Q7477|<math>\BernoullinumberB{2n} = (-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = (-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (- 1)^(n + 1)*(4*n)/(1 - (2)^(1 - 2*n))*int(((t)^(2*n - 1))/(exp(2*Pi*t)+ 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == (- 1)^(n + 1)*Divide[4*n,1 - (2)^(1 - 2*n)]*Integrate[Divide[(t)^(2*n - 1),Exp[2*Pi*t]+ 1], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/24.7.E1 24.7.E1] || <math qid="Q7477">\BernoullinumberB{2n} = (-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = (-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (- 1)^(n + 1)*(4*n)/(1 - (2)^(1 - 2*n))*int(((t)^(2*n - 1))/(exp(2*Pi*t)+ 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == (- 1)^(n + 1)*Divide[4*n,1 - (2)^(1 - 2*n)]*Integrate[Divide[(t)^(2*n - 1),Exp[2*Pi*t]+ 1], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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-| [https://dlmf.nist.gov/24.7.E1 24.7.E1] || [[Item:Q7477|<math>(-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\diff{t} = (-1)^{n+1}\frac{2n}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\sech@{\pi t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\diff{t} = (-1)^{n+1}\frac{2n}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\sech@{\pi t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(- 1)^(n + 1)*(4*n)/(1 - (2)^(1 - 2*n))*int(((t)^(2*n - 1))/(exp(2*Pi*t)+ 1), t = 0..infinity) = (- 1)^(n + 1)*(2*n)/(1 - (2)^(1 - 2*n))*int((t)^(2*n - 1)* exp(- Pi*t)*sech(Pi*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(- 1)^(n + 1)*Divide[4*n,1 - (2)^(1 - 2*n)]*Integrate[Divide[(t)^(2*n - 1),Exp[2*Pi*t]+ 1], {t, 0, Infinity}, GenerateConditions->None] == (- 1)^(n + 1)*Divide[2*n,1 - (2)^(1 - 2*n)]*Integrate[(t)^(2*n - 1)* Exp[- Pi*t]*Sech[Pi*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 3]
+| [https://dlmf.nist.gov/24.7.E1 24.7.E1] || <math qid="Q7477">(-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\diff{t} = (-1)^{n+1}\frac{2n}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\sech@{\pi t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(-1)^{n+1}\frac{4n}{1-2^{1-2n}}\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}+1}\diff{t} = (-1)^{n+1}\frac{2n}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\sech@{\pi t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(- 1)^(n + 1)*(4*n)/(1 - (2)^(1 - 2*n))*int(((t)^(2*n - 1))/(exp(2*Pi*t)+ 1), t = 0..infinity) = (- 1)^(n + 1)*(2*n)/(1 - (2)^(1 - 2*n))*int((t)^(2*n - 1)* exp(- Pi*t)*sech(Pi*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(- 1)^(n + 1)*Divide[4*n,1 - (2)^(1 - 2*n)]*Integrate[Divide[(t)^(2*n - 1),Exp[2*Pi*t]+ 1], {t, 0, Infinity}, GenerateConditions->None] == (- 1)^(n + 1)*Divide[2*n,1 - (2)^(1 - 2*n)]*Integrate[(t)^(2*n - 1)* Exp[- Pi*t]*Sech[Pi*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 3]
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-| [https://dlmf.nist.gov/24.7.E2 24.7.E2] || [[Item:Q7478|<math>\BernoullinumberB{2n} = (-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}-1}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = (-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}-1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (- 1)^(n + 1)* 4*n*int(((t)^(2*n - 1))/(exp(2*Pi*t)- 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == (- 1)^(n + 1)* 4*n*Integrate[Divide[(t)^(2*n - 1),Exp[2*Pi*t]- 1], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/24.7.E2 24.7.E2] || <math qid="Q7478">\BernoullinumberB{2n} = (-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}-1}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = (-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}-1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (- 1)^(n + 1)* 4*n*int(((t)^(2*n - 1))/(exp(2*Pi*t)- 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == (- 1)^(n + 1)* 4*n*Integrate[Divide[(t)^(2*n - 1),Exp[2*Pi*t]- 1], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
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-| [https://dlmf.nist.gov/24.7.E2 24.7.E2] || [[Item:Q7478|<math>(-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}-1}\diff{t} = (-1)^{n+1}2n\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\csch@{\pi t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}-1}\diff{t} = (-1)^{n+1}2n\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\csch@{\pi t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(- 1)^(n + 1)* 4*n*int(((t)^(2*n - 1))/(exp(2*Pi*t)- 1), t = 0..infinity) = (- 1)^(n + 1)* 2*n*int((t)^(2*n - 1)* exp(- Pi*t)*csch(Pi*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(- 1)^(n + 1)* 4*n*Integrate[Divide[(t)^(2*n - 1),Exp[2*Pi*t]- 1], {t, 0, Infinity}, GenerateConditions->None] == (- 1)^(n + 1)* 2*n*Integrate[(t)^(2*n - 1)* Exp[- Pi*t]*Csch[Pi*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 3]
+| [https://dlmf.nist.gov/24.7.E2 24.7.E2] || <math qid="Q7478">(-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}-1}\diff{t} = (-1)^{n+1}2n\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\csch@{\pi t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>(-1)^{n+1}4n\int_{0}^{\infty}\frac{t^{2n-1}}{e^{2\pi t}-1}\diff{t} = (-1)^{n+1}2n\int_{0}^{\infty}t^{2n-1}e^{-\pi t}\csch@{\pi t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(- 1)^(n + 1)* 4*n*int(((t)^(2*n - 1))/(exp(2*Pi*t)- 1), t = 0..infinity) = (- 1)^(n + 1)* 2*n*int((t)^(2*n - 1)* exp(- Pi*t)*csch(Pi*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>(- 1)^(n + 1)* 4*n*Integrate[Divide[(t)^(2*n - 1),Exp[2*Pi*t]- 1], {t, 0, Infinity}, GenerateConditions->None] == (- 1)^(n + 1)* 2*n*Integrate[(t)^(2*n - 1)* Exp[- Pi*t]*Csch[Pi*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Successful || Successful || Skip - symbolical successful subtest || Successful [Tested: 3]
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-| [https://dlmf.nist.gov/24.7.E3 24.7.E3] || [[Item:Q7479|<math>\BernoullinumberB{2n} = (-1)^{n+1}\frac{\pi}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n}\sech^{2}@{\pi t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = (-1)^{n+1}\frac{\pi}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n}\sech^{2}@{\pi t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (- 1)^(n + 1)*(Pi)/(1 - (2)^(1 - 2*n))*int((t)^(2*n)* (sech(Pi*t))^(2), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == (- 1)^(n + 1)*Divide[Pi,1 - (2)^(1 - 2*n)]*Integrate[(t)^(2*n)* (Sech[Pi*t])^(2), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 3] || Skipped - Because timed out
+| [https://dlmf.nist.gov/24.7.E3 24.7.E3] || <math qid="Q7479">\BernoullinumberB{2n} = (-1)^{n+1}\frac{\pi}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n}\sech^{2}@{\pi t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = (-1)^{n+1}\frac{\pi}{1-2^{1-2n}}\int_{0}^{\infty}t^{2n}\sech^{2}@{\pi t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (- 1)^(n + 1)*(Pi)/(1 - (2)^(1 - 2*n))*int((t)^(2*n)* (sech(Pi*t))^(2), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == (- 1)^(n + 1)*Divide[Pi,1 - (2)^(1 - 2*n)]*Integrate[(t)^(2*n)* (Sech[Pi*t])^(2), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 3] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/24.7.E4 24.7.E4] || [[Item:Q7480|<math>\BernoullinumberB{2n} = (-1)^{n+1}\pi\int_{0}^{\infty}t^{2n}\csch^{2}@{\pi t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = (-1)^{n+1}\pi\int_{0}^{\infty}t^{2n}\csch^{2}@{\pi t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (- 1)^(n + 1)* Pi*int((t)^(2*n)* (csch(Pi*t))^(2), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == (- 1)^(n + 1)* Pi*Integrate[(t)^(2*n)* (Csch[Pi*t])^(2), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 3] || Skipped - Because timed out
+| [https://dlmf.nist.gov/24.7.E4 24.7.E4] || <math qid="Q7480">\BernoullinumberB{2n} = (-1)^{n+1}\pi\int_{0}^{\infty}t^{2n}\csch^{2}@{\pi t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = (-1)^{n+1}\pi\int_{0}^{\infty}t^{2n}\csch^{2}@{\pi t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (- 1)^(n + 1)* Pi*int((t)^(2*n)* (csch(Pi*t))^(2), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == (- 1)^(n + 1)* Pi*Integrate[(t)^(2*n)* (Csch[Pi*t])^(2), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || Successful [Tested: 3] || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/24.7.E5 24.7.E5] || [[Item:Q7481|<math>\BernoullinumberB{2n} = (-1)^{n}\frac{2n(2n-1)}{\pi}\*\int_{0}^{\infty}t^{2n-2}\ln@{1-e^{-2\pi t}}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = (-1)^{n}\frac{2n(2n-1)}{\pi}\*\int_{0}^{\infty}t^{2n-2}\ln@{1-e^{-2\pi t}}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (- 1)^(n)*(2*n*(2*n - 1))/(Pi)* int((t)^(2*n - 2)* ln(1 - exp(- 2*Pi*t)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == (- 1)^(n)*Divide[2*n*(2*n - 1),Pi]* Integrate[(t)^(2*n - 2)* Log[1 - Exp[- 2*Pi*t]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
+| [https://dlmf.nist.gov/24.7.E5 24.7.E5] || <math qid="Q7481">\BernoullinumberB{2n} = (-1)^{n}\frac{2n(2n-1)}{\pi}\*\int_{0}^{\infty}t^{2n-2}\ln@{1-e^{-2\pi t}}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullinumberB{2n} = (-1)^{n}\frac{2n(2n-1)}{\pi}\*\int_{0}^{\infty}t^{2n-2}\ln@{1-e^{-2\pi t}}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n) = (- 1)^(n)*(2*n*(2*n - 1))/(Pi)* int((t)^(2*n - 2)* ln(1 - exp(- 2*Pi*t)), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n] == (- 1)^(n)*Divide[2*n*(2*n - 1),Pi]* Integrate[(t)^(2*n - 2)* Log[1 - Exp[- 2*Pi*t]], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Successful [Tested: 3] || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/24.7.E6 24.7.E6] || [[Item:Q7482|<math>\EulernumberE{2n} = (-1)^{n}2^{2n+1}\int_{0}^{\infty}t^{2n}\sech@{\pi t}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulernumberE{2n} = (-1)^{n}2^{2n+1}\int_{0}^{\infty}t^{2n}\sech@{\pi t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n) = (- 1)^(n)* (2)^(2*n + 1)* int((t)^(2*n)* sech(Pi*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n] == (- 1)^(n)* (2)^(2*n + 1)* Integrate[(t)^(2*n)* Sech[Pi*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 3]
+| [https://dlmf.nist.gov/24.7.E6 24.7.E6] || <math qid="Q7482">\EulernumberE{2n} = (-1)^{n}2^{2n+1}\int_{0}^{\infty}t^{2n}\sech@{\pi t}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulernumberE{2n} = (-1)^{n}2^{2n+1}\int_{0}^{\infty}t^{2n}\sech@{\pi t}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n) = (- 1)^(n)* (2)^(2*n + 1)* int((t)^(2*n)* sech(Pi*t), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n] == (- 1)^(n)* (2)^(2*n + 1)* Integrate[(t)^(2*n)* Sech[Pi*t], {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Missing Macro Error || Failure || - || Successful [Tested: 3]
 |-
-| [https://dlmf.nist.gov/24.7.E7 24.7.E7] || [[Item:Q7483|<math>\BernoullipolyB{2n}@{x} = (-1)^{n+1}2n\*\int_{0}^{\infty}\frac{\cos@{2\pi x}-e^{-2\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n-1}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{2n}@{x} = (-1)^{n+1}2n\*\int_{0}^{\infty}\frac{\cos@{2\pi x}-e^{-2\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n-1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n, x) = (- 1)^(n + 1)* 2*n * int((cos(2*Pi*x)- exp(- 2*Pi*t))/(cosh(2*Pi*t)- cos(2*Pi*x))*(t)^(2*n - 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n, x] == (- 1)^(n + 1)* 2*n * Integrate[Divide[Cos[2*Pi*x]- Exp[- 2*Pi*t],Cosh[2*Pi*t]- Cos[2*Pi*x]]*(t)^(2*n - 1), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1875000000
+| [https://dlmf.nist.gov/24.7.E7 24.7.E7] || <math qid="Q7483">\BernoullipolyB{2n}@{x} = (-1)^{n+1}2n\*\int_{0}^{\infty}\frac{\cos@{2\pi x}-e^{-2\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n-1}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{2n}@{x} = (-1)^{n+1}2n\*\int_{0}^{\infty}\frac{\cos@{2\pi x}-e^{-2\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n-1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n, x) = (- 1)^(n + 1)* 2*n * int((cos(2*Pi*x)- exp(- 2*Pi*t))/(cosh(2*Pi*t)- cos(2*Pi*x))*(t)^(2*n - 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n, x] == (- 1)^(n + 1)* 2*n * Integrate[Divide[Cos[2*Pi*x]- Exp[- 2*Pi*t],Cosh[2*Pi*t]- Cos[2*Pi*x]]*(t)^(2*n - 1), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [2 / 3]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .1875000000
 Test Values: {x = 3/2, n = 3}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: 6.000000000
 Test Values: {x = 2, n = 3}</syntaxhighlight><br></div></div> || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/24.7.E8 24.7.E8] || [[Item:Q7484|<math>\BernoullipolyB{2n+1}@{x} = (-1)^{n+1}(2n+1)\*\int_{0}^{\infty}\frac{\sin@{2\pi x}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{2n+1}@{x} = (-1)^{n+1}(2n+1)\*\int_{0}^{\infty}\frac{\sin@{2\pi x}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n + 1, x) = (- 1)^(n + 1)*(2*n + 1)* int((sin(2*Pi*x))/(cosh(2*Pi*t)- cos(2*Pi*x))*(t)^(2*n), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n + 1, x] == (- 1)^(n + 1)*(2*n + 1)* Integrate[Divide[Sin[2*Pi*x],Cosh[2*Pi*t]- Cos[2*Pi*x]]*(t)^(2*n), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7500000000
+| [https://dlmf.nist.gov/24.7.E8 24.7.E8] || <math qid="Q7484">\BernoullipolyB{2n+1}@{x} = (-1)^{n+1}(2n+1)\*\int_{0}^{\infty}\frac{\sin@{2\pi x}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{2n+1}@{x} = (-1)^{n+1}(2n+1)\*\int_{0}^{\infty}\frac{\sin@{2\pi x}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>bernoulli(2*n + 1, x) = (- 1)^(n + 1)*(2*n + 1)* int((sin(2*Pi*x))/(cosh(2*Pi*t)- cos(2*Pi*x))*(t)^(2*n), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[2*n + 1, x] == (- 1)^(n + 1)*(2*n + 1)* Integrate[Divide[Sin[2*Pi*x],Cosh[2*Pi*t]- Cos[2*Pi*x]]*(t)^(2*n), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .7500000000
 Test Values: {x = 3/2, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .3125000000
 Test Values: {x = 3/2, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/24.7.E9 24.7.E9] || [[Item:Q7485|<math>\EulerpolyE{2n}@{x} = (-1)^{n}4\int_{0}^{\infty}\frac{\sin@{\pi x}\cosh@{\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{2n}@{x} = (-1)^{n}4\int_{0}^{\infty}\frac{\sin@{\pi x}\cosh@{\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n, x) = (- 1)^(n)* 4*int((sin(Pi*x)*cosh(Pi*t))/(cosh(2*Pi*t)- cos(2*Pi*x))*(t)^(2*n), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n, x] == (- 1)^(n)* 4*Integrate[Divide[Sin[Pi*x]*Cosh[Pi*t],Cosh[2*Pi*t]- Cos[2*Pi*x]]*(t)^(2*n), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5000000001
+| [https://dlmf.nist.gov/24.7.E9 24.7.E9] || <math qid="Q7485">\EulerpolyE{2n}@{x} = (-1)^{n}4\int_{0}^{\infty}\frac{\sin@{\pi x}\cosh@{\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{2n}@{x} = (-1)^{n}4\int_{0}^{\infty}\frac{\sin@{\pi x}\cosh@{\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n, x) = (- 1)^(n)* 4*int((sin(Pi*x)*cosh(Pi*t))/(cosh(2*Pi*t)- cos(2*Pi*x))*(t)^(2*n), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n, x] == (- 1)^(n)* 4*Integrate[Divide[Sin[Pi*x]*Cosh[Pi*t],Cosh[2*Pi*t]- Cos[2*Pi*x]]*(t)^(2*n), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .5000000001
 Test Values: {x = 3/2, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .1249999998
 Test Values: {x = 3/2, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/24.7.E10 24.7.E10] || [[Item:Q7486|<math>\EulerpolyE{2n+1}@{x} = (-1)^{n+1}4\*\int_{0}^{\infty}\frac{\cos@{\pi x}\sinh@{\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n+1}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{2n+1}@{x} = (-1)^{n+1}4\*\int_{0}^{\infty}\frac{\cos@{\pi x}\sinh@{\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n+1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n + 1, x) = (- 1)^(n + 1)* 4 * int((cos(Pi*x)*sinh(Pi*t))/(cosh(2*Pi*t)- cos(2*Pi*x))*(t)^(2*n + 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n + 1, x] == (- 1)^(n + 1)* 4 * Integrate[Divide[Cos[Pi*x]*Sinh[Pi*t],Cosh[2*Pi*t]- Cos[2*Pi*x]]*(t)^(2*n + 1), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2499999999
+| [https://dlmf.nist.gov/24.7.E10 24.7.E10] || <math qid="Q7486">\EulerpolyE{2n+1}@{x} = (-1)^{n+1}4\*\int_{0}^{\infty}\frac{\cos@{\pi x}\sinh@{\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n+1}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\EulerpolyE{2n+1}@{x} = (-1)^{n+1}4\*\int_{0}^{\infty}\frac{\cos@{\pi x}\sinh@{\pi t}}{\cosh@{2\pi t}-\cos@{2\pi x}}t^{2n+1}\diff{t}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>euler(2*n + 1, x) = (- 1)^(n + 1)* 4 * int((cos(Pi*x)*sinh(Pi*t))/(cosh(2*Pi*t)- cos(2*Pi*x))*(t)^(2*n + 1), t = 0..infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>EulerE[2*n + 1, x] == (- 1)^(n + 1)* 4 * Integrate[Divide[Cos[Pi*x]*Sinh[Pi*t],Cosh[2*Pi*t]- Cos[2*Pi*x]]*(t)^(2*n + 1), {t, 0, Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Aborted || <div class="toccolours mw-collapsible mw-collapsed">Failed [6 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: .2499999999
 Test Values: {x = 3/2, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .6250000031e-1
 Test Values: {x = 3/2, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
 |-
-| [https://dlmf.nist.gov/24.7.E11 24.7.E11] || [[Item:Q7487|<math>\BernoullipolyB{n}@{x} = \frac{1}{2\pi i}\int_{-c-i\infty}^{-c+i\infty}(x+t)^{n}\left(\frac{\pi}{\sin@{\pi t}}\right)^{2}\diff{t}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{x} = \frac{1}{2\pi i}\int_{-c-i\infty}^{-c+i\infty}(x+t)^{n}\left(\frac{\pi}{\sin@{\pi t}}\right)^{2}\diff{t}</syntaxhighlight> || <math>0 < c, c < 1</math> || <syntaxhighlight lang=mathematica>bernoulli(n, x) = (1)/(2*Pi*I)*int((x + t)^(n)*((Pi)/(sin(Pi*t)))^(2), t = - c - I*infinity..- c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, x] == Divide[1,2*Pi*I]*Integrate[(x + t)^(n)*(Divide[Pi,Sin[Pi*t]])^(2), {t, - c - I*Infinity, - c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.
+| [https://dlmf.nist.gov/24.7.E11 24.7.E11] || <math qid="Q7487">\BernoullipolyB{n}@{x} = \frac{1}{2\pi i}\int_{-c-i\infty}^{-c+i\infty}(x+t)^{n}\left(\frac{\pi}{\sin@{\pi t}}\right)^{2}\diff{t}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\BernoullipolyB{n}@{x} = \frac{1}{2\pi i}\int_{-c-i\infty}^{-c+i\infty}(x+t)^{n}\left(\frac{\pi}{\sin@{\pi t}}\right)^{2}\diff{t}</syntaxhighlight> || <math>0 < c, c < 1</math> || <syntaxhighlight lang=mathematica>bernoulli(n, x) = (1)/(2*Pi*I)*int((x + t)^(n)*((Pi)/(sin(Pi*t)))^(2), t = - c - I*infinity..- c + I*infinity)</syntaxhighlight> || <syntaxhighlight lang=mathematica>BernoulliB[n, x] == Divide[1,2*Pi*I]*Integrate[(x + t)^(n)*(Divide[Pi,Sin[Pi*t]])^(2), {t, - c - I*Infinity, - c + I*Infinity}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || <div class="toccolours mw-collapsible mw-collapsed">Failed [7 / 9]<div class="mw-collapsible-content"><syntaxhighlight lang=mathematica>Result: 1.
 Test Values: {c = 1/2, x = 3/2, n = 1}</syntaxhighlight><br><syntaxhighlight lang=mathematica>Result: .9166666667
 Test Values: {c = 1/2, x = 3/2, n = 2}</syntaxhighlight><br>... skip entries to safe data</div></div> || Skipped - Because timed out
 |}
 </div>

24.7: Difference between revisions

Latest revision as of 12:02, 28 June 2021

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