若干重要积分的间接方法  

SPECIAL INDIRECT METHODS FOR SEVERAL IMPORTANT INTEGRALS

作　　者：周国全[1] 曾伟豪 喻成城 ZHOU Guoquan;ZENG Weihao;YU Chengcheng(School of Physics and Technology,Wuhan University,Wuhan,Hubei 430072)

机构地区：[1]武汉大学物理科学与技术学院,湖北武汉430072

出　　处：《物理与工程》2021年第3期8-12,共5页Physics and Engineering

基　　金：中央高校教育教学改革专向项目-武汉大学“351人才计划”教学岗位项目。

摘　　要：本文(1)将两个复杂而重要的含参无穷积分视为其参变量的函数,运用一致收敛的含参积分对参变量的可导性质,设法将问题转化为关于参变量的简单微分方程,从而间接而巧妙地求出积分结果;(2)对于n维空间的球体体积与表面积的问题,本文介绍一种移花接木的方法,巧妙地推导出n维球体的体积与表面积公式。In this paper,two complex and important infinite integrals with parameters are regarded as the functions of their parameters.Using of the differentiable property of consistently convergent integrals with respect to their parameters,we change these integrals into differential equations and calculate the integrals indirectly and tactfully.For the problem of volume and surface area of sphere in n-dimensional space,this paper introduces a method of transplanting flowers and trees,and deduces the formula of volume and surface area of n-dimensional sphere skillfully.Aided with Matlab integral program,above results are proved.

关 键 词：含参积分 一致收敛 微分方程 n维球体 体积公式 表面积公式 贝塞尔函数 汉克尔变换 

分 类 号：O172.2[理学—数学]