Example 9. Compare
the "discrete interpolation polynomial" and "shifted Legendre series
approximation"
9 (b). Use the
function
, on
the interval
.
Solution 9 (b).
![[Graphics:../Images/LegendrePolyMod_gr_384.gif]](../Images/LegendrePolyMod_gr_384.gif)
![[Graphics:../Images/LegendrePolyMod_gr_385.gif]](../Images/LegendrePolyMod_gr_385.gif)
Details for this computation.
First, construct the coefficients.
![[Graphics:../Images/LegendrePolyMod_gr_387.gif]](../Images/LegendrePolyMod_gr_387.gif)
Construct the terms.
![[Graphics:../Images/LegendrePolyMod_gr_389.gif]](../Images/LegendrePolyMod_gr_389.gif)
![[Graphics:../Images/LegendrePolyMod_gr_390.gif]](../Images/LegendrePolyMod_gr_390.gif)
Then add up the terms.
![[Graphics:../Images/LegendrePolyMod_gr_392.gif]](../Images/LegendrePolyMod_gr_392.gif)
(c) John H. Mathews 2005