Combinatorial Analysis - 26.12 Plane Partitions
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 26.12.E23 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\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) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 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)
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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]
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Failure | Aborted | Skipped - Because timed out | Skipped - Because timed out |
| 26.12#Ex7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemannzeta@{3} = 1.20205\;69032}
\Riemannzeta@{3} = 1.20205\;69032 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | Zeta(3) = 1.2020569032
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Zeta[3] == 1.2020569032
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Successful | Failure | - | Successful [Tested: 1] |
| 26.12#Ex8 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \Riemannzeta'@{-1} = -0.16542\;11437}
\Riemannzeta'@{-1} = -0.16542\;11437 |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | subs( temp=- 1, diff( Zeta(temp), temp$(1) ) ) = - 0.1654211437
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(D[Zeta[temp], {temp, 1}]/.temp-> - 1) == - 0.1654211437
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Successful | Failure | - | Successful [Tested: 1] |