Define the Fejer kernel by F(u)=1/n+1[D(u)+D1(u)+.....Dn(u)]. Assuming the result of part (a) show that F(u) =...

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Define the Fejer kernel by F(u)=1/n+1[D(u)+D1(u)+.....Dn(u)]. Assuming the result of part (a) show that F(u) = F(u): = [Do(u) + Di(u) + n+1 +1, + D(u)]. 1 [sin ((n + 1)u/2 at Du/2)], u#2jm, sin u=2jx for some integer j. Define the Fejer kernel by F(u)=1/n+1[D(u)+D1(u)+.....Dn(u)]. Assuming the result of part (a) show that F(u) = F(u): = [Do(u) + Di(u) + n+1 +1, + D(u)]. 1 [sin ((n + 1)u/2 at Du/2)], u#2jm, sin u=2jx for some integer j.

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