1.2: Difference between revisions

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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/1.2.E1 1.2.E1] || [[Item:Q30|<math>\binom{n}{k} = \frac{n!}{(n-k)!k!}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\binom{n}{k} = \frac{n!}{(n-k)!k!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/1.2.E1 1.2.E1] || <math qid="Q30">\binom{n}{k} = \frac{n!}{(n-k)!k!}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\binom{n}{k} = \frac{n!}{(n-k)!k!}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/1.2.E1 1.2.E1] || [[Item:Q30|<math>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(factorial(n))/(factorial(n - k)*factorial(k)) = binomial(n,n - k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(n)!,(n - k)!*(k)!] == Binomial[n,n - k]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
| [https://dlmf.nist.gov/1.2.E1 1.2.E1] || <math qid="Q30">\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{n!}{(n-k)!k!} = \binom{n}{n-k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>(factorial(n))/(factorial(n - k)*factorial(k)) = binomial(n,n - k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(n)!,(n - k)!*(k)!] == Binomial[n,n - k]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 9]
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| [https://dlmf.nist.gov/1.2.E6 1.2.E6] || [[Item:Q35|<math>\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((- 1)^(k)* pochhammer(- z, k))/(factorial(k)) = (- 1)^(k)*binomial(k - z - 1,k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(- 1)^(k)* Pochhammer[- z, k],(k)!] == (- 1)^(k)*Binomial[k - z - 1,k]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
| [https://dlmf.nist.gov/1.2.E6 1.2.E6] || <math qid="Q35">\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>((- 1)^(k)* pochhammer(- z, k))/(factorial(k)) = (- 1)^(k)*binomial(k - z - 1,k)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Divide[(- 1)^(k)* Pochhammer[- z, k],(k)!] == (- 1)^(k)*Binomial[k - z - 1,k]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
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| [https://dlmf.nist.gov/1.2.E7 1.2.E7] || [[Item:Q36|<math>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>binomial(z + 1,k) = binomial(z,k)+binomial(z,k - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Binomial[z + 1,k] == Binomial[z,k]+Binomial[z,k - 1]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
| [https://dlmf.nist.gov/1.2.E7 1.2.E7] || <math qid="Q36">\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>binomial(z + 1,k) = binomial(z,k)+binomial(z,k - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Binomial[z + 1,k] == Binomial[z,k]+Binomial[z,k - 1]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
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| [https://dlmf.nist.gov/1.2.E8 1.2.E8] || [[Item:Q37|<math>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(binomial(z + k,k), k = 0..m) = binomial(z + m + 1,m)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Binomial[z + k,k], {k, 0, m}, GenerateConditions->None] == Binomial[z + m + 1,m]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
| [https://dlmf.nist.gov/1.2.E8 1.2.E8] || <math qid="Q37">\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(binomial(z + k,k), k = 0..m) = binomial(z + m + 1,m)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Sum[Binomial[z + k,k], {k, 0, m}, GenerateConditions->None] == Binomial[z + m + 1,m]</syntaxhighlight> || Successful || Successful || - || Successful [Tested: 21]
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.2.E10 1.2.E10] || [[Item:Q39|<math>na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">n*a +(1)/(2)*n*(n - 1)*d = (1)/(2)*n*(a + ell)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">n*a +Divide[1,2]*n*(n - 1)*d == Divide[1,2]*n*(a + \[ScriptL])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.2.E10 1.2.E10] || <math qid="Q39">na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">n*a +(1)/(2)*n*(n - 1)*d = (1)/(2)*n*(a + ell)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">n*a +Divide[1,2]*n*(n - 1)*d == Divide[1,2]*n*(a + \[ScriptL])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.2.E22 1.2.E22] || [[Item:Q51|<math>M(r) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M(r) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r)) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r)) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.2.E22 1.2.E22] || <math qid="Q51">M(r) = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M(r) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r)) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">((Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r)) == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.2#Ex1 1.2#Ex1] || [[Item:Q54|<math>M(1) = A</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M(1) = A</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M(1) = ((a[1]+ a[2]+ .. + a[n])/(n))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M[1] == (Divide[Subscript[a, 1]+ Subscript[a, 2]+ \[Ellipsis]+ Subscript[a, n],n])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.2#Ex1 1.2#Ex1] || <math qid="Q54">M(1) = A</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M(1) = A</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M(1) = ((a[1]+ a[2]+ .. + a[n])/(n))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M[1] == (Divide[Subscript[a, 1]+ Subscript[a, 2]+ \[Ellipsis]+ Subscript[a, n],n])</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.2#Ex2 1.2#Ex2] || [[Item:Q55|<math>M(-1) = H</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M(-1) = H</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M(- 1) = H</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M[- 1] == H</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.2#Ex2 1.2#Ex2] || <math qid="Q55">M(-1) = H</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>M(-1) = H</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M(- 1) = H</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">M[- 1] == H</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/1.2.E26 1.2.E26] || [[Item:Q56|<math>\lim_{r\to 0}M(r) = G</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{r\to 0}M(r) = G</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r), r = 0) = ((a[1]*a[2] .. a[n])^(1/n))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[(Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r), r -> 0, GenerateConditions->None] == ((Subscript[a, 1]*Subscript[a, 2] \[Ellipsis]Subscript[a, n])^(1/n))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/1.2.E26 1.2.E26] || <math qid="Q56">\lim_{r\to 0}M(r) = G</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>\lim_{r\to 0}M(r) = G</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">limit((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r), r = 0) = ((a[1]*a[2] .. a[n])^(1/n))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Limit[(Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r), r -> 0, GenerateConditions->None] == ((Subscript[a, 1]*Subscript[a, 2] \[Ellipsis]Subscript[a, n])^(1/n))</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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Latest revision as of 10:58, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple
Symbolic
Mathematica
Numeric
Maple
Numeric
Mathematica
1.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{n}{k} = \frac{n!}{(n-k)!k!}}
\binom{n}{k} = \frac{n!}{(n-k)!k!}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
binomial(n,k) = (factorial(n))/(factorial(n - k)*factorial(k))
Binomial[n,k] == Divide[(n)!,(n - k)!*(k)!]
Successful Successful - Successful [Tested: 9]
1.2.E1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{n!}{(n-k)!k!} = \binom{n}{n-k}}
\frac{n!}{(n-k)!k!} = \binom{n}{n-k}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
(factorial(n))/(factorial(n - k)*factorial(k)) = binomial(n,n - k)
Divide[(n)!,(n - k)!*(k)!] == Binomial[n,n - k]
Successful Successful - Successful [Tested: 9]
1.2.E6 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}}
\frac{(-1)^{k}\Pochhammersym{-z}{k}}{k!} = (-1)^{k}\binom{k-z-1}{k}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
((- 1)^(k)* pochhammer(- z, k))/(factorial(k)) = (- 1)^(k)*binomial(k - z - 1,k)
Divide[(- 1)^(k)* Pochhammer[- z, k],(k)!] == (- 1)^(k)*Binomial[k - z - 1,k]
Successful Successful - Successful [Tested: 21]
1.2.E7 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}}
\binom{z+1}{k} = \binom{z}{k}+\binom{z}{k-1}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
binomial(z + 1,k) = binomial(z,k)+binomial(z,k - 1)
Binomial[z + 1,k] == Binomial[z,k]+Binomial[z,k - 1]
Successful Successful - Successful [Tested: 21]
1.2.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}}
\sum^{m}_{k=0}\binom{z+k}{k} = \binom{z+m+1}{m}
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
sum(binomial(z + k,k), k = 0..m) = binomial(z + m + 1,m)
Sum[Binomial[z + k,k], {k, 0, m}, GenerateConditions->None] == Binomial[z + m + 1,m]
Successful Successful - Successful [Tested: 21]
1.2.E10 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)}
na+\tfrac{1}{2}n(n-1)d = \tfrac{1}{2}n(a+\ell)
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
n*a +(1)/(2)*n*(n - 1)*d = (1)/(2)*n*(a + ell)
n*a +Divide[1,2]*n*(n - 1)*d == Divide[1,2]*n*(a + \[ScriptL])
Skipped - no semantic math Skipped - no semantic math - -
1.2.E22 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(r) = 0}
M(r) = 0
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r)) = 0
((Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r)) == 0
Skipped - no semantic math Skipped - no semantic math - -
1.2#Ex1 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(1) = A}
M(1) = A
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
M(1) = ((a[1]+ a[2]+ .. + a[n])/(n))
M[1] == (Divide[Subscript[a, 1]+ Subscript[a, 2]+ \[Ellipsis]+ Subscript[a, n],n])
Skipped - no semantic math Skipped - no semantic math - -
1.2#Ex2 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle M(-1) = H}
M(-1) = H
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
M(- 1) = H
M[- 1] == H
Skipped - no semantic math Skipped - no semantic math - -
1.2.E26 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle \lim_{r\to 0}M(r) = G}
\lim_{r\to 0}M(r) = G
Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle }
limit((p[1]*(a[1])^(r)+ p[2]*(a[2])^(r)+ .. + p[n]*(a[n])^(r))^(1/r), r = 0) = ((a[1]*a[2] .. a[n])^(1/n))
Limit[(Subscript[p, 1]*(Subscript[a, 1])^(r)+ Subscript[p, 2]*(Subscript[a, 2])^(r)+ \[Ellipsis]+ Subscript[p, n]*(Subscript[a, n])^(r))^(1/r), r -> 0, GenerateConditions->None] == ((Subscript[a, 1]*Subscript[a, 2] \[Ellipsis]Subscript[a, n])^(1/n))
Skipped - no semantic math Skipped - no semantic math - -