View source for 16.8

{{DISPLAYTITLE:Generalized Hypergeometric Functions & Meijer G -Function - 16.8 Differential Equations}}

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! scope="col" style="position: sticky; top: 0;" | Formula 
! 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
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! scope="col" style="position: sticky; top: 0;" | Numeric<br>Mathematica
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| [https://dlmf.nist.gov/16.8.E4 16.8.E4] || [[Item:Q5222|<math>z^{q}D^{q+1}w+\sum_{j=1}^{q}z^{j-1}(\alpha_{j}z+\beta_{j})D^{j}w+\alpha_{0}w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z^{q}D^{q+1}w+\sum_{j=1}^{q}z^{j-1}(\alpha_{j}z+\beta_{j})D^{j}w+\alpha_{0}w = 0</syntaxhighlight> || <math>p \leq q</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(z)^(q)* (D)^(q + 1)* w + sum((z)^(j - 1)*(alpha[j]*z + beta[j])*(D)^(j)* w , j = 1..q)+ alpha[0]*w = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(z)^(q)* (D)^(q + 1)* w + Sum[(z)^(j - 1)*(Subscript[\[Alpha], j]*z + Subscript[\[Beta], j])*(D)^(j)* w , {j, 1, q}, GenerateConditions->None]+ Subscript[\[Alpha], 0]*w == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/16.8.E5 16.8.E5] || [[Item:Q5223|<math>z^{q}(1-z)D^{q+1}w+\sum_{j=1}^{q}z^{j-1}(\alpha_{j}z+\beta_{j})D^{j}w+\alpha_{0}w = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>z^{q}(1-z)D^{q+1}w+\sum_{j=1}^{q}z^{j-1}(\alpha_{j}z+\beta_{j})D^{j}w+\alpha_{0}w = 0</syntaxhighlight> || <math>p = q+1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(z)^(q)*(1 - z)*(D)^(q + 1)* w + sum((z)^(j - 1)*(alpha[j]*z + beta[j])*(D)^(j)* w , j = 1..q)+ alpha[0]*w = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">(z)^(q)*(1 - z)*(D)^(q + 1)* w + Sum[(z)^(j - 1)*(Subscript[\[Alpha], j]*z + Subscript[\[Beta], j])*(D)^(j)* w , {j, 1, q}, GenerateConditions->None]+ Subscript[\[Alpha], 0]*w == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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