18.30: 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/18.30.E1 18.30.E1] || [[Item:Q5998|<math>A_{n}A_{n+1}C_{n+1} > 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{n}A_{n+1}C_{n+1} > 0</syntaxhighlight> || <math>n \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[n]*A[n + 1]*C[n + 1] > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, n]*Subscript[A, n + 1]*Subscript[C, n + 1] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/18.30.E1 18.30.E1] || <math qid="Q5998">A_{n}A_{n+1}C_{n+1} > 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A_{n}A_{n+1}C_{n+1} > 0</syntaxhighlight> || <math>n \geq 0</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A[n]*A[n + 1]*C[n + 1] > 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[A, n]*Subscript[A, n + 1]*Subscript[C, n + 1] > 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/18.30#Ex1 18.30#Ex1] || [[Item:Q5999|<math>p_{-1}(x;c) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{-1}(x;c) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[- 1](x ; c) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, - 1][x ; c] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/18.30#Ex1 18.30#Ex1] || <math qid="Q5999">p_{-1}(x;c) = 0</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{-1}(x;c) = 0</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[- 1](x ; c) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, - 1][x ; c] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/18.30#Ex2 18.30#Ex2] || [[Item:Q6000|<math>p_{0}(x;c) = 1</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{0}(x;c) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[0](x ; c) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, 0][x ; c] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/18.30#Ex2 18.30#Ex2] || <math qid="Q6000">p_{0}(x;c) = 1</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{0}(x;c) = 1</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[0](x ; c) = 1</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, 0][x ; c] == 1</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/18.30.E3 18.30.E3] || [[Item:Q6001|<math>p_{n+1}(x;c) = (A_{n+c}x+B_{n+c})p_{n}(x;c)-C_{n+c}p_{n-1}(x;c)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{n+1}(x;c) = (A_{n+c}x+B_{n+c})p_{n}(x;c)-C_{n+c}p_{n-1}(x;c)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[n + 1](x ; c) = (A[n + c]*x + B[n + c])*p[n](x ; c)- C[n + c]*p[n - 1](x ; c)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, n + 1][x ; c] == (Subscript[A, n + c]*x + Subscript[B, n + c])*Subscript[p, n][x ; c]- Subscript[C, n + c]*Subscript[p, n - 1][x ; c]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
| [https://dlmf.nist.gov/18.30.E3 18.30.E3] || <math qid="Q6001">p_{n+1}(x;c) = (A_{n+c}x+B_{n+c})p_{n}(x;c)-C_{n+c}p_{n-1}(x;c)</math><br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>p_{n+1}(x;c) = (A_{n+c}x+B_{n+c})p_{n}(x;c)-C_{n+c}p_{n-1}(x;c)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">p[n + 1](x ; c) = (A[n + c]*x + B[n + c])*p[n](x ; c)- C[n + c]*p[n - 1](x ; c)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[p, n + 1][x ; c] == (Subscript[A, n + c]*x + Subscript[B, n + c])*Subscript[p, n][x ; c]- Subscript[C, n + c]*Subscript[p, n - 1][x ; c]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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Latest revision as of 11:47, 28 June 2021


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
18.30.E1 A n ⁢ A n + 1 ⁢ C n + 1 > 0 subscript 𝐴 𝑛 subscript 𝐴 𝑛 1 subscript 𝐶 𝑛 1 0 {\displaystyle{\displaystyle A_{n}A_{n+1}C_{n+1}>0}}
A_{n}A_{n+1}C_{n+1} > 0		 n ≥ 0 𝑛 0 {\displaystyle{\displaystyle n\geq 0}} 
A[n]*A[n + 1]*C[n + 1] > 0
 
Subscript[A, n]*Subscript[A, n + 1]*Subscript[C, n + 1] > 0
 Skipped - no semantic math Skipped - no semantic math - -
18.30#Ex1 p - 1 ⁢ ( x ; c ) = 0 subscript 𝑝 1 𝑥 𝑐 0 {\displaystyle{\displaystyle p_{-1}(x;c)=0}}
p_{-1}(x;c) = 0		 

p[- 1](x ; c) = 0
 
Subscript[p, - 1][x ; c] == 0
 Skipped - no semantic math Skipped - no semantic math - -
18.30#Ex2 p 0 ⁢ ( x ; c ) = 1 subscript 𝑝 0 𝑥 𝑐 1 {\displaystyle{\displaystyle p_{0}(x;c)=1}}
p_{0}(x;c) = 1		 

p[0](x ; c) = 1
 
Subscript[p, 0][x ; c] == 1
 Skipped - no semantic math Skipped - no semantic math - -
18.30.E3 p n + 1 ⁢ ( x ; c ) = ( A n + c ⁢ x + B n + c ) ⁢ p n ⁢ ( x ; c ) - C n + c ⁢ p n - 1 ⁢ ( x ; c ) subscript 𝑝 𝑛 1 𝑥 𝑐 subscript 𝐴 𝑛 𝑐 𝑥 subscript 𝐵 𝑛 𝑐 subscript 𝑝 𝑛 𝑥 𝑐 subscript 𝐶 𝑛 𝑐 subscript 𝑝 𝑛 1 𝑥 𝑐 {\displaystyle{\displaystyle p_{n+1}(x;c)=(A_{n+c}x+B_{n+c})p_{n}(x;c)-C_{n+c}% p_{n-1}(x;c)}}
p_{n+1}(x;c) = (A_{n+c}x+B_{n+c})p_{n}(x;c)-C_{n+c}p_{n-1}(x;c)		 

p[n + 1](x ; c) = (A[n + c]*x + B[n + c])*p[n](x ; c)- C[n + c]*p[n - 1](x ; c)
 
Subscript[p, n + 1][x ; c] == (Subscript[A, n + c]*x + Subscript[B, n + c])*Subscript[p, n][x ; c]- Subscript[C, n + c]*Subscript[p, n - 1][x ; c]
 Skipped - no semantic math Skipped - no semantic math - -
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