| 半无界空间上函数的傅里叶-贝塞尔积分展开 |
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| 引用本文： | 姜向前,侯春风,孟庆鑫,张宇.半无界空间上函数的傅里叶-贝塞尔积分展开[J].大学物理,2020(5):14-15,26. |
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| 作者姓名： | 姜向前 侯春风 孟庆鑫 张宇 |
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| 作者单位： | 哈尔滨工业大学物理学院 |
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| 基金项目： | 高等学校数学物理方法课程教学研究项目资助。 |
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| 摘 要： | 柱坐标系中,本征函数族贝塞尔函数构成完备正交系,因此可作为广义傅里叶级数展开的基.本文从定义在有限区间0,ρ0]上函数的广义傅里叶级数展开出发,利用贝塞尔函数的渐近展开公式以及贝塞尔函数零点的近似公式,讨论了半无界空间上函数的傅里叶-贝塞尔积分展开问题,得到了本征函数模方的近似表达式.当ρ0趋于无穷时,不连续参量变成连续参量,得到了函数的傅里叶-贝塞尔积分及其展开系数公式.
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| 关 键 词： | 贝塞尔函数 傅里叶-贝塞尔积分 |
The Fourier-Bessel integral expansion of a function in semi-infinite space |
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| JIANG Xiang-qian,HOU Chun-feng,MENG Qing-xin,ZHANG Yu.The Fourier-Bessel integral expansion of a function in semi-infinite space[J].College Physics,2020(5):14-15,26. |
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| Authors: | JIANG Xiang-qian HOU Chun-feng MENG Qing-xin ZHANG Yu |
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| Institution: | (School of Physics,Harbin Institute of Technology,Harbin,Heilongjiang 150001,China) |
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| Abstract: | In cylindrical coordinates, the family of intrinsic Bessel function constitutes a complete orthogonal function series, which can be used as the bases of generalized Fourier expansion. In this paper, starting from the generalized Fourier expansion of a function defined on a finite interval and using the approximate formula of Bessel function and its zero point formula, we discuss the Fourier-Bessel integral expansion of a function defined in semi-infinite space, and get the approximate expression of module square of Bessel function. In the asymptotical situation, discontinuous parameter becomes continuous one, we obtain the Fourier-Bessel integral and coefficient formula of the function. |
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| Keywords: | Bessel function Fourier-Bessel integral |
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