广义泰勒中值定理中间点的一个渐近估计式

An asymptotic estimation formula of the intermediate point for generalized Taylor mean value theorem

中值定理只给出了“中间点”在某区间内的存在性,并没有指出“中间点”在某区间内的位置.通过对中值定理“中间点”渐近性的研究可以确定“中间点”在某区间内的渐近位置,因此研究“中间点”的渐近性有一定理论意义.在无穷区间上研究广义泰勒中值定理“中间点”当区间长度趋近于无穷时的渐近性态,在一定条件下,建立了广义泰勒中值定理“中间点”当区间长度趋近于无穷时一个新的渐近估计式,并举例说明新渐近估计式的有效性和广泛性,从而推广和改进了有关文献中的一些结果.

The mean value theorem only gives the existence of intermediate point in an interval, and does not point out the position of intermediate point in an interval. Through the study of the asymptotic behavior of the intermediate point in the mean value theorem, the asymptotic position of the intermediate point in an interval can be determined, so it is of certain theoretical significance to study the asymptotic property of the intermediate point. In the infinite interval, the asymptotic behavior of the generalized Taylor mean value theorem intermediate point is studied when the interval length approaches infinity. Under certain conditions, a new asymptotic estimation formula of the generalized Taylor mean value theorem intermediate point is established when the interval length approaches infinity. An example is also given to illustrate the validity and universality of the result of this paper. The results in this paper improve and extend the corresponding results of some reference.