The moments of the weight functions $w(x)=e^{-x}x^\mu(\ln x)^\rho$, $\rho=0, 1, 2$, on $[0, \infty)$ with respect to the Confluent Hypergeometric function $\phi(a - n, c;x)$, $n = 0, 1, 2, \cdots$, are explicitly evaluated.