| 浅析广义积分inttegral from n=+ to ∞(f(x)dx)收敛的必要条件 |
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| 引用本文： | 杜素勤.浅析广义积分inttegral from n=+ to ∞(f(x)dx)收敛的必要条件[J].安庆师范学院学报(自然科学版),2004(4). |
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| 作者姓名： | 杜素勤 |
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| 作者单位： | 三明高等专科学校数学系 福建三明 365004 |
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| 摘 要： | 广义积分收敛的必要条件具体地说为:若函数f(x)在a,b]上黎曼可积,则f(x)在a,b]上有界且几乎处处连续,而当f(x)的无限广义积分收敛时,则f(x)在其广义积分收敛的区域内几乎处处连续但不一定有界。若无穷级数收敛,则其一般项必收敛于0,而当f(x)的无限广义积分收敛时,f(x)却不一定收敛于0(当x趋于无穷大时),要使f(x)收敛于0(x→∞),还需附加一定的条件。
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| 关 键 词： | 积分 收敛 极限 有界 无界 |
On the Necessary Conditions for Convergence of Generalized Integral inttegral from n=+ to ∞(f(x)dx) |
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| DU Su-qin.On the Necessary Conditions for Convergence of Generalized Integral inttegral from n=+ to ∞(f(x)dx)[J].Journal of Anqing Teachers College(Natural Science Edition),2004(4). |
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| Authors: | DU Su-qin |
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| Abstract: | This paper deals with the necessary conditions for convergence of integral.It further explains:if function f(x) can be integrate in Riemman way in a,b],then f(x) is bounded and almost everywhere continuous function in a,b],but if generalized integral of function f(x) converges,then f(x) continue almost everywhere in the intervevl of its convergence,and we can't make sure f(x) is a bounded function.If infinite series converges ,then its general term converges 0,but if generalized integral of the function f(x) converges,then f(x) converges 0 uncertainly(when x→∞),and if we want to make f(x) converges 0(x→∞),we must add certain terms. |
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| Keywords: | integral convergence limit bounded sum unbounded sum |
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