基于PBV条件下正弦与余弦积分的收敛性

Convergence of Sine and Cosine Integrals under PBV Condition

基于文献[2]中的思想,将系数数列的PBV条件推广到函数的PBV条件,分别给出了PBV条件下正弦积分与余弦积分一致收敛性的充分必要条件(见定理1和定理2),并利用Cauchy收敛准则、分部积分等一些数学技巧去证明,最后给出了PBV条件中一个性质不可缺少的例子。

This paper promotes PBV condition of coefficient series to PBV condition of function based on the thought in literature [2] and respectively gives necessary and sufficient conditions of uniform convergence of sine and cosine integrals under PBV condition （see theorems 1 and 2）; demonstrates them with some mathematical techniques such as Cauchy convergence criterion and integration by parts and finally gives an example of indispensable property in PBV condition.