Matching derivatives at zero produces a polynomial approximation to . Every additional odd-power term captures another derivative; for any fixed finite interval, the sequence converges to the sine curve.在零点匹配各阶导数，可以构造 的多项式近似。每增加一个奇次幂项，就匹配更高阶导数；在任意固定的有限区间上，这组近似收敛到正弦曲线。
The cyan curve is . The green polynomial uses one through five terms in turn: agreement appears first near zero and extends outward.青色曲线是 ，绿色多项式依次使用一至五项。近似先在零点附近吻合，再逐渐向两侧延伸。