View source for 19.19

{{DISPLAYTITLE:Elliptic Integrals - 19.19 Taylor and Related Series}}

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! scope="col" style="position: sticky; top: 0;" | DLMF 
! scope="col" style="position: sticky; top: 0;" | Formula 
! scope="col" style="position: sticky; top: 0;" | Constraints 
! scope="col" style="position: sticky; top: 0;" | Maple
! scope="col" style="position: sticky; top: 0;" | Mathematica
! 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/19.19#Ex1 19.19#Ex1] || [[Item:Q6368|<math>A = \frac{1}{n}\sum_{j=1}^{n}z_{j}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>A = \frac{1}{n}\sum_{j=1}^{n}z_{j}</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A = (1)/(n)*sum(z[j], j = 1..n)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">A == Divide[1,n]*Sum[Subscript[z, j], {j, 1, n}, GenerateConditions->None]</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/19.19#Ex2 19.19#Ex2] || [[Item:Q6369|<math>Z_{j} = 1-(z_{j}/A)</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>Z_{j} = 1-(z_{j}/A)</syntaxhighlight> || <math></math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Z[j] = 1 -(z[j]/A)</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[Z, j] == 1 -(Subscript[z, j]/A)</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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| [https://dlmf.nist.gov/19.19#Ex3 19.19#Ex3] || [[Item:Q6370|<math>E_{1}(\mathbf{Z}) = 0</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%; background: inherit;" inline>E_{1}(\mathbf{Z}) = 0</syntaxhighlight> || <math>|Z_{j}| < 1</math> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">E[1](Z) = 0</pre></div> || <div class="mw-highlight mw-highlight-lang-mathematica mw-content-ltr" dir="ltr"><pre style="background: inherit;">Subscript[E, 1][Z] == 0</pre></div> || Skipped - no semantic math || Skipped - no semantic math || - || -
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