论文标题
基于样条的正弦和正弦，余弦和正弦积分的任意准确界限
Spline Based Series for Sine and Arbitrarily Accurate Bounds for Sine, Cosine and Sine Integral
论文作者
论文摘要
基于两点样条的近似值，在间隔[0，pi/2]上定义了SIN（X）和SIN（X）/X的下限的一系列函数，其相对误差越低，相对较小的相对误差比已发布的结果越来越小。第二，第四和第八阶近似值分别具有3.31 x 10-4、2.48 x 10-8和2.02 x 10-18的间隔[0，pi/2]的最大相对误差。提出了正弦函数的新序列，其收敛明显更好，即在间隔[0，pi/2]上的泰勒序列。应用程序包括正弦函数的上限，余弦函数的上限和下限的功能以及正弦积分函数的下限。这些有限的功能可以任意准确。
Based on two point spline approximations of arbitrary order, a series of functions that define lower bounds for sin(x) and sin(x)/x, over the interval [0,Pi/2], with increasingly low relative errors and smaller relative errors than published results, are defined. Second, fourth and eighth order approximations have, respectively, maximum relative errors over the interval [0,Pi/2] of 3.31 x 10-4, 2.48 x 10-8, and 2.02 x 10-18. New series for the sine function, which have significantly better convergence that a Taylor series over the interval [0,Pi/2], are proposed. Applications include functions that are upper bounds for the sine function, upper and lower bounds for the cosine function and lower bounds for the sine integral function. These bounded functions can be made arbitrarily accurate.
