26.11: 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/26.11.E2 26.11.E2] || [[Item:Q7905|<math>\ncompositions[m]@{0} = \Kroneckerdelta{0}{m}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ncompositions[m]@{0} = \Kroneckerdelta{0}{m}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>numbcomp(0, m) = KroneckerDelta[0, m]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/26.11.E2 26.11.E2] || <math qid="Q7905">\ncompositions[m]@{0} = \Kroneckerdelta{0}{m}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ncompositions[m]@{0} = \Kroneckerdelta{0}{m}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>numbcomp(0, m) = KroneckerDelta[0, m]</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Error || Missing Macro Error || - || -
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| [https://dlmf.nist.gov/26.11.E3 26.11.E3] || [[Item:Q7906|<math>\ncompositions[m]@{n} = \binom{n-1}{m-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ncompositions[m]@{n} = \binom{n-1}{m-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>numbcomp(n, m) = binomial(n - 1,m - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/26.11.E3 26.11.E3] || <math qid="Q7906">\ncompositions[m]@{n} = \binom{n-1}{m-1}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\ncompositions[m]@{n} = \binom{n-1}{m-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>numbcomp(n, m) = binomial(n - 1,m - 1)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Error || Missing Macro Error || - || -
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| [https://dlmf.nist.gov/26.11.E4 26.11.E4] || [[Item:Q7907|<math>\sum_{n=0}^{\infty}\ncompositions[m]@{n}q^{n} = \frac{q^{m}}{(1-q)^{m}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\ncompositions[m]@{n}q^{n} = \frac{q^{m}}{(1-q)^{m}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(numbcomp(n, m)*(q)^(n), n = 0..infinity) = ((q)^(m))/((1 - q)^(m))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Error || Missing Macro Error || - || -
| [https://dlmf.nist.gov/26.11.E4 26.11.E4] || <math qid="Q7907">\sum_{n=0}^{\infty}\ncompositions[m]@{n}q^{n} = \frac{q^{m}}{(1-q)^{m}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>\sum_{n=0}^{\infty}\ncompositions[m]@{n}q^{n} = \frac{q^{m}}{(1-q)^{m}}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>sum(numbcomp(n, m)*(q)^(n), n = 0..infinity) = ((q)^(m))/((1 - q)^(m))</syntaxhighlight> || <syntaxhighlight lang=mathematica>Error</syntaxhighlight> || Error || Missing Macro Error || - || -
|- style="background: #dfe6e9;"
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| [https://dlmf.nist.gov/26.11#Ex1 26.11#Ex1] || [[Item:Q7908|<math>F_{0} = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>F_{0} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">F[0] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[F, 0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/26.11#Ex1 26.11#Ex1] || <math qid="Q7908">F_{0} = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>F_{0} = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">F[0] = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[F, 0] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/26.11#Ex2 26.11#Ex2] || [[Item:Q7909|<math>F_{1} = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>F_{1} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">F[1] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[F, 1] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/26.11#Ex2 26.11#Ex2] || <math qid="Q7909">F_{1} = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>F_{1} = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">F[1] = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[F, 1] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/26.11#Ex3 26.11#Ex3] || [[Item:Q7910|<math>F_{n} = F_{n-1}+F_{n-2}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>F_{n} = F_{n-1}+F_{n-2}</syntaxhighlight> || <math>n \geq 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">F[n] = F[n - 1]+ F[n - 2]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[F, n] == Subscript[F, n - 1]+ Subscript[F, n - 2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/26.11#Ex3 26.11#Ex3] || <math qid="Q7910">F_{n} = F_{n-1}+F_{n-2}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>F_{n} = F_{n-1}+F_{n-2}</syntaxhighlight> || <math>n \geq 2</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">F[n] = F[n - 1]+ F[n - 2]</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[F, n] == Subscript[F, n - 1]+ Subscript[F, n - 2]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
|- style="background: #dfe6e9;"
|- style="background: #dfe6e9;"
| [https://dlmf.nist.gov/26.11.E7 26.11.E7] || [[Item:Q7912|<math>F_{n} = \frac{(1+\sqrt{5})^{n}-(1-\sqrt{5})^{n}}{2^{n}\,\sqrt{5}}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>F_{n} = \frac{(1+\sqrt{5})^{n}-(1-\sqrt{5})^{n}}{2^{n}\,\sqrt{5}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">F[n] = ((1 +sqrt(5))^(n)-(1 -sqrt(5))^(n))/((2)^(n)*sqrt(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[F, n] == Divide[(1 +Sqrt[5])^(n)-(1 -Sqrt[5])^(n),(2)^(n)*Sqrt[5]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/26.11.E7 26.11.E7] || <math qid="Q7912">F_{n} = \frac{(1+\sqrt{5})^{n}-(1-\sqrt{5})^{n}}{2^{n}\,\sqrt{5}}</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>F_{n} = \frac{(1+\sqrt{5})^{n}-(1-\sqrt{5})^{n}}{2^{n}\,\sqrt{5}}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">F[n] = ((1 +sqrt(5))^(n)-(1 -sqrt(5))^(n))/((2)^(n)*sqrt(5))</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[F, n] == Divide[(1 +Sqrt[5])^(n)-(1 -Sqrt[5])^(n),(2)^(n)*Sqrt[5]]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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Latest revision as of 12:06, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
26.11.E2 c m ⁡ ( 0 ) = δ 0 , m number-of-compositions-C-into-parts 𝑚 0 Kronecker 0 𝑚 {\displaystyle{\displaystyle c_{m}\left(0\right)=\delta_{0,m}}}
\ncompositions[m]@{0} = \Kroneckerdelta{0}{m}		 

numbcomp(0, m) = KroneckerDelta[0, m]

Error
Error Missing Macro Error - -
26.11.E3 c m ⁡ ( n ) = ( n - 1 m - 1 ) number-of-compositions-C-into-parts 𝑚 𝑛 binomial 𝑛 1 𝑚 1 {\displaystyle{\displaystyle c_{m}\left(n\right)=\genfrac{(}{)}{0.0pt}{}{n-1}{% m-1}}}
\ncompositions[m]@{n} = \binom{n-1}{m-1}		 

numbcomp(n, m) = binomial(n - 1,m - 1)

Error
Error Missing Macro Error - -
26.11.E4 ∑ n = 0 ∞ c m ⁡ ( n ) ⁢ q n = q m ( 1 - q ) m superscript subscript 𝑛 0 number-of-compositions-C-into-parts 𝑚 𝑛 superscript 𝑞 𝑛 superscript 𝑞 𝑚 superscript 1 𝑞 𝑚 {\displaystyle{\displaystyle\sum_{n=0}^{\infty}c_{m}\left(n\right)q^{n}=\frac{% q^{m}}{(1-q)^{m}}}}
\sum_{n=0}^{\infty}\ncompositions[m]@{n}q^{n} = \frac{q^{m}}{(1-q)^{m}}		 

sum(numbcomp(n, m)*(q)^(n), n = 0..infinity) = ((q)^(m))/((1 - q)^(m))

Error
Error Missing Macro Error - -
26.11#Ex1 F 0 = 0 subscript 𝐹 0 0 {\displaystyle{\displaystyle F_{0}=0}}
F_{0} = 0		 

F[0] = 0
 
Subscript[F, 0] == 0
 Skipped - no semantic math Skipped - no semantic math - -
26.11#Ex2 F 1 = 1 subscript 𝐹 1 1 {\displaystyle{\displaystyle F_{1}=1}}
F_{1} = 1		 

F[1] = 1
 
Subscript[F, 1] == 1
 Skipped - no semantic math Skipped - no semantic math - -
26.11#Ex3 F n = F n - 1 + F n - 2 subscript 𝐹 𝑛 subscript 𝐹 𝑛 1 subscript 𝐹 𝑛 2 {\displaystyle{\displaystyle F_{n}=F_{n-1}+F_{n-2}}}
F_{n} = F_{n-1}+F_{n-2}		 n ≥ 2 𝑛 2 {\displaystyle{\displaystyle n\geq 2}} 
F[n] = F[n - 1]+ F[n - 2]
 
Subscript[F, n] == Subscript[F, n - 1]+ Subscript[F, n - 2]
 Skipped - no semantic math Skipped - no semantic math - -
26.11.E7 F n = ( 1 + 5 ) n - ( 1 - 5 ) n 2 n ⁢ 5 subscript 𝐹 𝑛 superscript 1 5 𝑛 superscript 1 5 𝑛 superscript 2 𝑛 5 {\displaystyle{\displaystyle F_{n}=\frac{(1+\sqrt{5})^{n}-(1-\sqrt{5})^{n}}{2^% {n}\,\sqrt{5}}}}
F_{n} = \frac{(1+\sqrt{5})^{n}-(1-\sqrt{5})^{n}}{2^{n}\,\sqrt{5}}		 

F[n] = ((1 +sqrt(5))^(n)-(1 -sqrt(5))^(n))/((2)^(n)*sqrt(5))
 
Subscript[F, n] == Divide[(1 +Sqrt[5])^(n)-(1 -Sqrt[5])^(n),(2)^(n)*Sqrt[5]]
 Skipped - no semantic math Skipped - no semantic math - -
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