Question: Suppose that X = { x i } j = 0 n is a nodal set of size n + 1 N in the compact

Suppose thatX={xi}j=0n is a nodal set of sizen+1N in the compact interval[a,b]R andx={i}j=0nPn is the Lagrange basis subordinate to X. Prove that if0mn then

I=0nximLi(x)=xm,xR

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