The obtained results in the paper are as follows : ( 1 ) the expansion of fourier series of orthogonal trigonometric polynomial for conditional mathematical expectation and function of random variable ; ( 2 ) the best approximation of trigonometric polynomial about another random variable for function of a random variable ; ( 3 ) the best approximation order of trigonometric polynomial for function of random variable 摘要获得了如下结果： ( 1 )条件数学期望及随机变量函数的三角多项式级数表达； ( 2 )一个随机变量关于另一个随机变量的三角多项式的最佳逼近； ( 3 )随机变量函数被随机变量三角多项式最佳逼近的阶。
