Example 9. Compare
the "discrete interpolation polynomial" and "shifted Legendre series
approximation"
9 (a). Use the
function
, on
the interval
.
Solution 9 (a).
![[Graphics:../Images/LegendrePolyMod_gr_374.gif]](../Images/LegendrePolyMod_gr_374.gif)
![[Graphics:../Images/LegendrePolyMod_gr_375.gif]](../Images/LegendrePolyMod_gr_375.gif)
Details for this computation.
First, construct the coefficients.
![[Graphics:../Images/LegendrePolyMod_gr_377.gif]](../Images/LegendrePolyMod_gr_377.gif)
Construct the terms.
![[Graphics:../Images/LegendrePolyMod_gr_379.gif]](../Images/LegendrePolyMod_gr_379.gif)
![[Graphics:../Images/LegendrePolyMod_gr_380.gif]](../Images/LegendrePolyMod_gr_380.gif)
Then add up the terms.
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(c) John H. Mathews 2005