【摘要】 考虑一类欧拉积分的计算问题,利用对参变量求导的方法,给出了欧拉积分公式的简短证明.利用欧拉积分公式,给出了菲涅尔积分和广义菲涅尔积分的一种简单的计算方法.利用积分交换次序定理,给出了一类广义积分的计算结果.对相关几类广义积分的计算给出了统一的计算方法,沟通了几类广义积分之间的相互联系.更多还原

【Abstract】 In order to solve the computational problem about a class of Euler integrals,this paper presents a simplified proof of Euler integrals formula by using a method in which the derivative of improper integrals with variable can be calculated.Based on the Euler integral formula,a simple method is provided for calculating Fresnel integrals and generalized Fresnel integrals.The calculation results of a class of improper integral are obtained by another method in which the order of quadratic integral can be exchanged.A uniform calculating method on several classes of related improper integrals is given for discussing the relationship between them.更多还原