Question

prove that the sum of langrange coefficient's is 1​

Answer 1

Answer:

Prove that the sum of the Lagrange (interpolation) coefficients is equal to 1.

Please suggest me a book-reference or give a solution for me. Thanks a lot in advance.

If  f=∑ni=0f(xi)Li(x)  then one has to prove ∑ni=0Li(x)=1 where Li(x)=(x−x0)...(x−xi−1)(x−xi+1)...(x−xn)(xi−x0)...(xi−xi−1)(xi−xi+1)...(xi−xn), i=0⋯n

polynomials numerical-methods

Explanation: