反常积分敛散性的新对数判别法 |
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引用本文: | 赵建华.反常积分敛散性的新对数判别法[J].河北煤炭建筑工程学院学报,2012(2):108-112. |
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作者姓名: | 赵建华 |
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作者单位: | 上海海事大学,上海200135 |
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摘 要: | 在很多实际问题中,要突破积分区间的有穷性和被积函数的有界性,由此得到了定积分的两种形式的推广:无穷限反常积分和瑕积分。我们将这两种积分统称为反常积分。因为反常积分涉及到一个收敛问题,所以反常积分敛散性的判定就显得非常重要了。本文就讨论了一种判定反常积分敛散性的新的对数判别法,并证明了这种新的对数判别法比旧的对数判别法更加精细。
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关 键 词: | 反常积分 敛散性 新判别法 |
New logarithmetic criteria of convergence of improper integrals |
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Affiliation: | ZHAO Jian - hua ( Shanghai Maritime University, Shanghai 200135 ,China) |
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Abstract: | In many practical problems, we must break through the finite interval of integral and the boundedness of integrand function, and consequently we get two forms of improper integrals: the im- proper integral in an infinite interval and the improper integral of an unbounded function. Because improper integrals are related to convergence, therefore, the determination of convergence and diver- gence of improper integrals are very important. This work discusses a new logarithmetic criterion for improper integrals, and proves that the new logarithmetic criterion is more precise than the old logarithetic criteria. |
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Keywords: | improper integrals convergence and divergence new criteria |
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