| 对数三角函数的定积分 |
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| 引用本文： | 邱为钢,唐荣荣.对数三角函数的定积分[J].大学数学,2011,27(5):134-137. |
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| 作者姓名： | 邱为钢 唐荣荣 |
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| 作者单位： | 湖州师范学院理学院,浙江湖州,313000 |
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| 基金项目： | 湖州师范学院高等教育研究项目，浙江省高等学校创新团队，湖州师范学院省级精品课程“高等数学” |
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| 摘 要： | 定义了三种积分表示的两元函数.这些两元函数有伽马函数表示,可以展开为幂级数.在积分符号内展开被积函数,先积分,再求和,也得到级数展开.对比展开系数,就得到一些对数三角函数定积分的值.选取合适的围道,得到其他两类对数三角函数定积分的值.
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| 关 键 词： | 伽马函数 对数三角函数 定积分 |
Definite Integral of Logarithm Trigonometric Function |
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| QIU Wei-gang.Definite Integral of Logarithm Trigonometric Function[J].College Mathematics,2011,27(5):134-137. |
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| Authors: | QIU Wei-gang |
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| Institution: | QIU Wei-gang(School of Science,Huzhou Teacher's College,Huzhou,Zhejiang 313000,China) |
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| Abstract: | The integral definition of three kind of two vatibles functions are given. These functions, in term of Gamma function. , can be expanded into power series. The integrand can also be expanded into powers series and integrated term by term. Comparing the power series coefficients, some definite integrals of logarithm trigonometric function is obtained. Other kind of logarithm trigonometric function integration are also evaluated by contour integral methods. |
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| Keywords: | Gamma function logarithm trigonometric function definite integral |
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