23.9: 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/23.9.E5 23.9.E5] || [[Item:Q7295|<math>c_{n} = \frac{3}{(2n+1)(n-3)}\sum_{m=2}^{n-2}c_{m}c_{n-m}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{n} = \frac{3}{(2n+1)(n-3)}\sum_{m=2}^{n-2}c_{m}c_{n-m}</syntaxhighlight> || <math>n \geq 4</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[n] = (3)/((2*n + 1)*(n - 3))*sum(c[m]*c[n - m], m = 2..n - 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, n] == Divide[3,(2*n + 1)*(n - 3)]*Sum[Subscript[c, m]*Subscript[c, n - m], {m, 2, n - 2}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/23.9.E5 23.9.E5] || <math qid="Q7295">c_{n} = \frac{3}{(2n+1)(n-3)}\sum_{m=2}^{n-2}c_{m}c_{n-m}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>c_{n} = \frac{3}{(2n+1)(n-3)}\sum_{m=2}^{n-2}c_{m}c_{n-m}</syntaxhighlight> || <math>n \geq 4</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">c[n] = (3)/((2*n + 1)*(n - 3))*sum(c[m]*c[n - m], m = 2..n - 2)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[c, n] == Divide[3,(2*n + 1)*(n - 3)]*Sum[Subscript[c, m]*Subscript[c, n - m], {m, 2, n - 2}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/23.9.E8 23.9.E8] || [[Item:Q7298|<math>a_{m,n} = 3(m+1)a_{m+1,n-1}+\tfrac{16}{3}(n+1)a_{m-2,n+1}-\tfrac{1}{3}(2m+3n-1)(4m+6n-1)a_{m-1,n}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{m,n} = 3(m+1)a_{m+1,n-1}+\tfrac{16}{3}(n+1)a_{m-2,n+1}-\tfrac{1}{3}(2m+3n-1)(4m+6n-1)a_{m-1,n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[m , n] = 3*(m + 1)*a[m + 1 , n - 1]+(16)/(3)*(n + 1)*a[m - 2 , n + 1]-(1)/(3)*(2*m + 3*n - 1)*(4*m + 6*n - 1)*a[m - 1 , n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, m , n] == 3*(m + 1)*Subscript[a, m + 1 , n - 1]+Divide[16,3]*(n + 1)*Subscript[a, m - 2 , n + 1]-Divide[1,3]*(2*m + 3*n - 1)*(4*m + 6*n - 1)*Subscript[a, m - 1 , n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/23.9.E8 23.9.E8] || <math qid="Q7298">a_{m,n} = 3(m+1)a_{m+1,n-1}+\tfrac{16}{3}(n+1)a_{m-2,n+1}-\tfrac{1}{3}(2m+3n-1)(4m+6n-1)a_{m-1,n}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>a_{m,n} = 3(m+1)a_{m+1,n-1}+\tfrac{16}{3}(n+1)a_{m-2,n+1}-\tfrac{1}{3}(2m+3n-1)(4m+6n-1)a_{m-1,n}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">a[m , n] = 3*(m + 1)*a[m + 1 , n - 1]+(16)/(3)*(n + 1)*a[m - 2 , n + 1]-(1)/(3)*(2*m + 3*n - 1)*(4*m + 6*n - 1)*a[m - 1 , n]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[a, m , n] == 3*(m + 1)*Subscript[a, m + 1 , n - 1]+Divide[16,3]*(n + 1)*Subscript[a, m - 2 , n + 1]-Divide[1,3]*(2*m + 3*n - 1)*(4*m + 6*n - 1)*Subscript[a, m - 1 , n]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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Latest revision as of 12:00, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
23.9.E5 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle c_{n} = \frac{3}{(2n+1)(n-3)}\sum_{m=2}^{n-2}c_{m}c_{n-m}}
c_{n} = \frac{3}{(2n+1)(n-3)}\sum_{m=2}^{n-2}c_{m}c_{n-m}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle n \geq 4} 
c[n] = (3)/((2*n + 1)*(n - 3))*sum(c[m]*c[n - m], m = 2..n - 2)
 
Subscript[c, n] == Divide[3,(2*n + 1)*(n - 3)]*Sum[Subscript[c, m]*Subscript[c, n - m], {m, 2, n - 2}, GenerateConditions->None]
 Skipped - no semantic math Skipped - no semantic math - -
23.9.E8 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle a_{m,n} = 3(m+1)a_{m+1,n-1}+\tfrac{16}{3}(n+1)a_{m-2,n+1}-\tfrac{1}{3}(2m+3n-1)(4m+6n-1)a_{m-1,n}}
a_{m,n} = 3(m+1)a_{m+1,n-1}+\tfrac{16}{3}(n+1)a_{m-2,n+1}-\tfrac{1}{3}(2m+3n-1)(4m+6n-1)a_{m-1,n}		 Failed to parse (LaTeXML (experimental; uses MathML): Invalid response ("") from server "http://latexml:8080/convert/":): {\displaystyle } 
a[m , n] = 3*(m + 1)*a[m + 1 , n - 1]+(16)/(3)*(n + 1)*a[m - 2 , n + 1]-(1)/(3)*(2*m + 3*n - 1)*(4*m + 6*n - 1)*a[m - 1 , n]
 
Subscript[a, m , n] == 3*(m + 1)*Subscript[a, m + 1 , n - 1]+Divide[16,3]*(n + 1)*Subscript[a, m - 2 , n + 1]-Divide[1,3]*(2*m + 3*n - 1)*(4*m + 6*n - 1)*Subscript[a, m - 1 , n]
 Skipped - no semantic math Skipped - no semantic math - -
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