Approximation to probability density functions in sampling distributions based on Fourier cosine series

We give a simple and precise approximation to probability density functions in sampling distributions based on Fourier cosine series. After clarifying the required conditions, two examples are illustrated. One is the distribution of a sum of random variables uniformly distributed as the probability density function has an explicit expression. The other is the distribution of sample skewness of random variables normally distributed as the probability density function has no explicit expression.