【摘要】 对数项级数及积分的柯西收敛准则的单调性和非负性进行推广。主要针对分组有界变差(GBV)条件的非负性作进一步研究,利用GBV性质及巧妙的分割方法给出最终适用条件的数列的柯西并项准则;同时,将系数数列的GBV条件推广到函数的GBV条件,最终给出分组有界变差函数GBVF的柯西并项准则。更多还原

【Abstract】 It is to generalize the monotonicity and positivity of Cauchy’s convergence criterion for numerical series and integral.It aims to do further research on the positivity of group bounded variation(GBV)and to offer the Cauchy’s condensation criterion for series.Moreover,its gives the final applicable conditions by using GBV property and ingenious segmentation method.Meanwhile,the GBV conditions is generalized from coefficient series to function so as to finally offer the Cauchy’s condensation criterion for group bounded variation function.更多还原