关键词： 含参变量广义积分, 欧拉积分公式, 内闭一致收敛性, 菲涅尔积分, 广义菲涅尔积分

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.

Key words: improper integrals with variable, Euler integral formula, inner close uniformly convergence, Fresnel integrals, generalized Fresnel integrals