待定系数法在三角函数积分计算中的应用

Undetermined Coefficient Methods' Applications to Computation of the Integral on Trigonometric Functions

运用复分析方法,首次给出了一类由三角函数、指数函数与幂函数乘积的线性组合产生的函数在某个区间上恒为零的充分必要条件证明,建立了此类函数积分计算的理论基础,结合微分和线性代数思想,系统讨论了待定系数法在一类含有三角函数的积分计算中的应用.

By using complex analytic method, a sufficient and necessary condition for a class of functions composed of the linear combination of products of trigonometric functions, exponential and power functions, which are identical with zero on some interval, are firstly proved, theory base on the integral computation is established. Combining with differential and linear algebra, undetermined coefficient methods＇ application to computations of a class of integral on trigonometric functions are systematic discussed.