  An analytical result is given for the exact evaluation of an integral which
arises in the analysis of acoustic radiation from wave packet sources:
  $
  I_{mn}(\beta,q) =
  \int_{-\infty}^{\infty}
  e^{-\beta^{2}x^{2}-i q x}x^{m+1/2}J_{n+1/2}(x)
  \,d x, $ where $m$ and $n$ are non-negative integers, and $J_{n+1/2}(\cdot)$
is a Bessel function of order $n+1/2$.
