关于麦克劳林公式中余项的注记

Annotations on the Form of Remainder in the Maclaurin Formula

结合具体例子讨论了麦克劳林公式中的余项形式,指出对于给定的麦克劳林多项式,用定义(直接法)获得的余项形式不唯一.利用常见初等函数的麦克劳林公式(间接法)得到的余项形式被讨论,该余项形式可能不是麦克劳林公式中的余项,但具有误差分析的价值.最后,建议在教材中引入“函数的n阶麦克劳林多项式”称谓,用于区别“n次麦克劳林多项式”,补充余项细节,降低学习难度.

The form of remainder in the Maclaurin formula is discussed by examples.It is pointed out that the remainder obtained by the definition(the direct method)is not unique for a given Maclaurin polynomial.The remainder obtained by using the Maclaurin formula(the indirect method)of an elementary functions is discussed.The remainder form may not be the remainder of the Maclaurin formula,but it has the value in the error analysis.Finally,it is suggested to define“the Maclaurin polynomial of order n”in the textbook to distinguish“the Maclaurin polynomial of degree n”,to reduce the reading difficulties by adding the details of the remainder.