View source for 18.30

{{DISPLAYTITLE:Orthogonal Polynomials - 18.30 Associated OP’s}}

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! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
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! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Maple
! scope="col" style="position: sticky; top: 0;" | Symbolic<br>Mathematica
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Maple
! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [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] || <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] || <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] || <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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