对数函数与幂函数的序关系及其应用

The Order Relationship between Logarithmic Function and Power Function and Its Application

给出了对数函数与幂函数的七种序关系,举例说明了这些序关系在判别反常积分和无穷级数敛散性中的应用.实践表明,应用这些序关系能准确地为含有对数函数因子的反常积分和无穷级数找到合适的比较对象,从而能对其敛散性做出正确的判断.

Seven order relation between logarithmic function and power function are given,and these order relation are applied in identifying convergent and divergent on improper integral and infinite series. In fact, using these order relation can accurately to find the right object for improper integral and infinite series that contain logarithmic function factor, which can make the correct judgment in its divergence.