View source for 36.12

{{DISPLAYTITLE:Integrals with Coalescing Saddles - 36.12 Uniform Approximation of Integrals}}

<div style="width: 100%; height: 75vh; overflow: auto;">
{| class="wikitable sortable" style="margin: 0;"
|-
! 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
|- 
| [https://dlmf.nist.gov/36.12.E9 36.12.E9] || [[Item:Q10001|<math>P_{mn}(\mathbf{y}) = (t_{n}(\mathbf{x}(\mathbf{y})))^{K+1}+\sum_{l=m+2}^{K}\frac{l}{K+2}x_{l}(\mathbf{y})(t_{n}(\mathbf{x}(\mathbf{y})))^{l-1}</math>]]<br><syntaxhighlight lang="tex" style="font-size: 75%;" inline>P_{mn}(\mathbf{y}) = (t_{n}(\mathbf{x}(\mathbf{y})))^{K+1}+\sum_{l=m+2}^{K}\frac{l}{K+2}x_{l}(\mathbf{y})(t_{n}(\mathbf{x}(\mathbf{y})))^{l-1}</syntaxhighlight> || <math></math> || <syntaxhighlight lang=mathematica>P[m, n](y) = (t[n](x(y)))^(K + 1)+ sum((l)/(K + 2)*x[l](y)*(t[n](x(y)))^(l - 1), l = m + 2..K)</syntaxhighlight> || <syntaxhighlight lang=mathematica>Subscript[P, m, n][y] == (Subscript[t, n][x[y]])^(K + 1)+ Sum[Divide[l,K + 2]*Subscript[x, l][y]*(Subscript[t, n][x[y]])^(l - 1), {l, m + 2, K}, GenerateConditions->None]</syntaxhighlight> || Failure || Failure || Skipped - Because timed out || Skipped - Because timed out
|}
</div>