LChrisman/Computing Derivatives for MetaLog

This page outlines an algorithm for computing the [math]\displaystyle{ i^{th} }[/math] derivative of a Keelin MetaLog.

Algorithm

1. For each [math]\displaystyle{ j=0 \mbox{to} i }[/math]
   • Compute [math]\displaystyle{ C_j = \left( \begin{array}{c}i \\ j\end{array}\right) ( i-j-1)! }[/math]
   • Compute [math]\displaystyle{ s^{(j)}(u) }[/math]
   • Compute [math]\displaystyle{ R(u) = (0.5+u)^j (0.5-u)^j }[/math]
   • Compute [math]\displaystyle{ N(u) = (0.5+u)^{i-j} - (-1)^{i-j} ( 0.5-u)^{i-j} }[/math]
   • Compute [math]\displaystyle{ T_j(u) = C_j \cdot s^{(j)}(u) \cdot R(u) \cdot N(u) }[/math]
2. [math]\displaystyle{ T(u) = \sum_{j=0}^i T_j(u) }[/math]