Title: An integral formula for the powered sum of the independent, identically and normally distributed random variables,
Abstract: The distribution of the sum of r-th power of standard normal random variables
is a generalization of the chi-squared distribution. In this paper, we
represent the probability density function of the random variable by an
one-dimensional absolutely convergent integral with the characteristic
function. Our integral formula is expected to be applied for evaluation of the
density function. Our integral formula is based on the inversion formula, and
we utilize a summation method. We also discuss on our formula in the view point
of hyperfunctions.