参数展开法及一类反常积分的计算

摘要

Some definite integrals of trigonometric functions with parameters can be calculated by the contour integral method. In the form of Gamma function, these integrals can be expanded into power series of parameters. On the other hand, the integrand can have a power series expansion about its parameters where the coefficients are definite integrals of logarithmic trigonometric functions. Certain definite integrals can be evaluated by comparing the two coefficients.%由围道积分得到了含参数三角函数的定积分.这个定积分通过伽马函数组合来表示,可以展开为参数的幂级数.同时在积分符号内对参数展开,展开系数为含对数三角函数的定积分.对比这两种参数展开的系数,得到了一些定积分的值.