  Quantum theory is awash in multidimensional integrals that contain
exponentials in the integration variables, their inverses, and inverse
polynomials of those variables. The present paper introduces a means to reduce
pairs of such integrals to one dimension when the integrand contains powers
times an arbitrary function of xy/(x+y) multiplying various combinations of
exponentials. In some cases these exponentials arise directly from
transition-amplitudes involving products of plane waves, hydrogenic wave
functions, Yukawa and/or Coulomb potentials. In other cases these exponentials
arise from Gaussian transforms of such functions.
