Combinatorial Analysis - 26.12 Plane Partitions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
26.12.E23	${\displaystyle{\displaystyle\prod_{h=1}^{r}\frac{1-q^{3h-1}}{1-q^{3h-2}}\prod_{1\leq h<j\leq r}\frac{1-q^{3(h+2j-1)}}{1-q^{3(h+j-1)}}=\prod_{h=1}^{r}\left(\frac{1-q^{3h-1}}{1-q^{3h-2}}\prod_{j=h}^{r}\frac{1-q^{3(r+h+j-1)}}{1-q^{3(2h+j-1)}}\right)}}$ \prod_{h=1}^{r}\frac{1-q^{3h-1}}{1-q^{3h-2}}\prod_{1\leq h<j\leq r}\frac{1-q^{3(h+2j-1)}}{1-q^{3(h+j-1)}} = \prod_{h=1}^{r}\left(\frac{1-q^{3h-1}}{1-q^{3h-2}}\prod_{j=h}^{r}\frac{1-q^{3(r+h+j-1)}}{1-q^{3(2h+j-1)}}\right)		product((1 - (q)^(3*h - 1))/(1 - (q)^(3*h - 2)), h = 1..r)*product(product((1 - (q)^(3*(h + 2*j - 1)))/(1 - (q)^(3*(h + j - 1))), j = h + 1..r), h = 1..j - 1) = product((1 - (q)^(3*h - 1))/(1 - (q)^(3*h - 2))*product((1 - (q)^(3*(r + h + j - 1)))/(1 - (q)^(3*(2*h + j - 1))), j = h..r), h = 1..r)	Product[Divide[1 - (q)^(3*h - 1),1 - (q)^(3*h - 2)], {h, 1, r}, GenerateConditions->None]*Product[Product[Divide[1 - (q)^(3*(h + 2*j - 1)),1 - (q)^(3*(h + j - 1))], {j, h + 1, r}, GenerateConditions->None], {h, 1, j - 1}, GenerateConditions->None] == Product[Divide[1 - (q)^(3*h - 1),1 - (q)^(3*h - 2)]*Product[Divide[1 - (q)^(3*(r + h + j - 1)),1 - (q)^(3*(2*h + j - 1))], {j, h, r}, GenerateConditions->None], {h, 1, r}, GenerateConditions->None]	Failure	Aborted	Skipped - Because timed out	Skipped - Because timed out
26.12#Ex7	${\displaystyle{\displaystyle\zeta\left(3\right)=1.20205\;69032}}$ \Riemannzeta@{3} = 1.20205\;69032		Zeta(3) = 1.2020569032	Zeta[3] == 1.2020569032	Successful	Failure	-	Successful [Tested: 1]
26.12#Ex8	${\displaystyle{\displaystyle\zeta'\left(-1\right)=-0.16542\;11437}}$ \Riemannzeta'@{-1} = -0.16542\;11437		subs( temp=- 1, diff( Zeta(temp), temp$(1) ) ) = - 0.1654211437	(D[Zeta[temp], {temp, 1}]/.temp-> - 1) == - 0.1654211437	Successful	Failure	-	Successful [Tested: 1]