| 一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算 |
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| 引用本文： | 赵剑威,吴志勤,雒秋明.一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算[J].大学数学,2005(1). |
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| 作者姓名： | 赵剑威 吴志勤 雒秋明 |
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| 作者单位： | 河南省教育信息中心 郑州450003
(赵剑威)，许昌学院数学系 许昌461000
(吴志勤)，焦作大学电大部 焦作454003(雒秋明) |
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| 摘 要： | 利用三角函数幂公式、L′Hospital法则、分部积分公式,得到含有三角函数的第一类广义积分integral from n=0 to ∞(((sin(θ_x))/x)~ndx)的计算公式,其中n≥1且θ≠0.
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| 关 键 词： | 广义积分 三角函数幂公式 L′Hospital法则 分部积分 数学归纳法 |
Some Evaluations for the First Kind of Improper Integralintegral from n=0 to ∞(((sin(θ_x))/x)~ndx) |
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| ZHAO Jian-wei,WU Zhi-qin,LUO Qiu-ming.Some Evaluations for the First Kind of Improper Integralintegral from n=0 to ∞(((sin(θ_x))/x)~ndx)[J].College Mathematics,2005(1). |
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| Authors: | ZHAO Jian-wei WU Zhi-qin LUO Qiu-ming |
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| Institution: | ZHAO Jian-wei~1,WU Zhi-qin~2,LUO Qiu-ming~3 |
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| Abstract: | Evaluations of the first kind of improper integrals ∫~∞_0sin(θx)x~ndx for positive integer n≥1 and θ≠0 are established using the trigonometric power formulae, the L′Hospital rule, integration by part, and mathematical induction. |
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| Keywords: | improper integral trigonometric power formula L′Hospital rule integration by part mathematical induction |
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