Combinatorial Analysis - 26.9 Integer Partitions:
Jump to navigation
Jump to search
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 26.9.E4 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \qbinom{m}{n}{q} = \prod_{j=1}^{n}\frac{1-q^{m-n+j}}{1-q^{j}}}
\qbinom{m}{n}{q} = \prod_{j=1}^{n}\frac{1-q^{m-n+j}}{1-q^{j}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n \geq 0} | QBinomial(m, n, q) = product((1 - (q)^(m - n + j))/(1 - (q)^(j)), j = 1..n)
|
QBinomial[m,n,q] == Product[Divide[1 - (q)^(m - n + j),1 - (q)^(j)], {j, 1, n}, GenerateConditions->None]
|
Failure | Failure | Error | Failed [32 / 90]
Result: DirectedInfinity[]
Test Values: {Rule[m, 1], Rule[n, 1], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
Result: DirectedInfinity[]
Test Values: {Rule[m, 2], Rule[n, 2], Rule[q, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}
... skip entries to safe data |
| 26.9.E5 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \prod_{j=1}^{k}\frac{1}{1-q^{j}} = 1+\sum_{m=1}^{\infty}\qbinom{k+m-1}{m}{q}q^{m}}
\prod_{j=1}^{k}\frac{1}{1-q^{j}} = 1+\sum_{m=1}^{\infty}\qbinom{k+m-1}{m}{q}q^{m} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | product((1)/(1 - (q)^(j)), j = 1..k) = 1 + sum(QBinomial(k + m - 1, m, q)*(q)^(m), m = 1..infinity)
|
Product[Divide[1,1 - (q)^(j)], {j, 1, k}, GenerateConditions->None] == 1 + Sum[QBinomial[k + m - 1,m,q]*(q)^(m), {m, 1, Infinity}, GenerateConditions->None]
|
Failure | Aborted | Error | Skipped - Because timed out |
| 26.9.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle 1+\sum_{k=1}^{\infty}\qbinom{m+k}{k}{q}x^{k} = \prod_{j=0}^{m}\frac{1}{1-x\,q^{j}}}
1+\sum_{k=1}^{\infty}\qbinom{m+k}{k}{q}x^{k} = \prod_{j=0}^{m}\frac{1}{1-x\,q^{j}} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | 1 + sum(QBinomial(m + k, k, q)*(x)^(k), k = 1..infinity) = product((1)/(1 - x*(q)^(j)), j = 0..m)
|
1 + Sum[QBinomial[m + k,k,q]*(x)^(k), {k, 1, Infinity}, GenerateConditions->None] == Product[Divide[1,1 - x*(q)^(j)], {j, 0, m}, GenerateConditions->None]
|
Failure | Aborted | Error | Skipped - Because timed out |