Example 9.  Compare the "discrete interpolation polynomial" and "shifted Legendre series approximation"
9 (b).  Use the function  [Graphics:Images/LegendrePolyMod_gr_371.gif],  on the interval  [Graphics:Images/LegendrePolyMod_gr_372.gif].  

Solution 9 (b).

[Graphics:../Images/LegendrePolyMod_gr_383.gif]



[Graphics:../Images/LegendrePolyMod_gr_384.gif]

[Graphics:../Images/LegendrePolyMod_gr_385.gif]

 

 

 

Details for this computation.

First, construct the coefficients.

[Graphics:../Images/LegendrePolyMod_gr_386.gif]


[Graphics:../Images/LegendrePolyMod_gr_387.gif]

 

 

Construct the terms.

[Graphics:../Images/LegendrePolyMod_gr_388.gif]



[Graphics:../Images/LegendrePolyMod_gr_389.gif]

[Graphics:../Images/LegendrePolyMod_gr_390.gif]

 

 

Then add up the terms.

[Graphics:../Images/LegendrePolyMod_gr_391.gif]


[Graphics:../Images/LegendrePolyMod_gr_392.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2005