In this paper, we consider the probability density function (pdf) of the weighted non-central chi-
square distribution with degrees of freedom. This pdf is presented in the literature as an infinite
sum. Consequently we give another expression for this pdf in terms of a generalized
hypergeometric function, modified Bessel function, and hyperbolic cosine function. Also, the
moment is obtained. In addition, we give two alternative expressions to the part of the pdf of the
even terms with odd number of degrees of freedom . Kettani's results (2006) can be obtained as a
special case of our results.