The paper introduces a modifing triangle interpolation polynomial Wn(f;r,θ) (where r is a given natural number) based on these values of f(θ) (where f(θ)∈C2π and f(θ) is an odd function) on these nodes {θk=k/(n+1)π}nk=1. Wn(f;r,θ) uniformly converges to f(θ)(f(θ)∈C2π and f(θ) is an odd function) on the total real axis. The approximation order of Wn(f;r,θ) reaches the best approximation order when used to approximate to f(θ) where f(θ)∈Cj2π(0≤ j ≤ r - 1) and f (θ) is an odd function. |