Algebraic and Analytic Methods - 1.7 Inequalities
| DLMF | Formula | Constraints | Maple | Mathematica | Symbolic Maple |
Symbolic Mathematica |
Numeric Maple |
Numeric Mathematica |
|---|---|---|---|---|---|---|---|---|
| 1.7.E1 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right)}
\left(\sum^{n}_{j=1}a_{j}b_{j}\right)^{2} \leq \left(\sum^{n}_{j=1}a_{j}^{2}\right)\left(\sum^{n}_{j=1}b_{j}^{2}\right) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (sum(a[j]*b[j], j = 1..n))^(2) <= (sum((a[j])^(2), j = 1..n))*(sum((b[j])^(2), j = 1..n)) |
((Sum[Subscript[a, j]*Subscript[b, j], {j, 1, n}, GenerateConditions->None]))^(2) <= (Sum[(Subscript[a, j])^(2), {j, 1, n}, GenerateConditions->None])*(Sum[(Subscript[b, j])^(2), {j, 1, n}, GenerateConditions->None]) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.7.E2 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q}}
\sum^{n}_{j=1}a_{j}b_{j} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}\left(\sum^{n}_{j=1}b_{j}^{q}\right)^{1/q} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | sum(a[j]*b[j], j = 1..n) <= (sum((a[j])^(p), j = 1..n))^(1/p)*(sum((b[j])^(q), j = 1..n))^(1/q) |
Sum[Subscript[a, j]*Subscript[b, j], {j, 1, n}, GenerateConditions->None] <= ((Sum[(Subscript[a, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)*((Sum[(Subscript[b, j])^(q), {j, 1, n}, GenerateConditions->None]))^(1/q) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.7.E3 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p}}
\left(\sum^{n}_{j=1}(a_{j}+b_{j})^{p}\right)^{1/p} \leq \left(\sum^{n}_{j=1}a_{j}^{p}\right)^{1/p}+\left(\sum^{n}_{j=1}b_{j}^{p}\right)^{1/p} |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | (sum((a[j]+ b[j])^(p), j = 1..n))^(1/p) <= (sum((a[j])^(p), j = 1..n))^(1/p)+(sum((b[j])^(p), j = 1..n))^(1/p) |
((Sum[(Subscript[a, j]+ Subscript[b, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p) <= ((Sum[(Subscript[a, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p)+((Sum[(Subscript[b, j])^(p), {j, 1, n}, GenerateConditions->None]))^(1/p) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.7.E7 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle H \leq G}
H \leq G |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } | H <= ((a[1]*a[2] .. a[n])^(1/n)) |
H <= ((Subscript[a, 1]*Subscript[a, 2] \[Ellipsis]Subscript[a, n])^(1/n)) |
Skipped - no semantic math | Skipped - no semantic math | - | - |
| 1.7.E9 | Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(r) \leq M(s)}
M(r) \leq M(s) |
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle r < s} | ((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r)) <= M(s) |
((Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r)) <= M[s] |
Skipped - no semantic math | Skipped - no semantic math | - | - |