  We have derived the integral form of the cusp and node coalescence conditions
satisfied by the wavefunction at the coalescence of two charged particles in $D
\geq 2$ dimension space. From it we have obtained the differential form of the
coalescence conditions. These expressions reduce to the well-known integral and
differential coalescence conditions in $D = 3$ space. It follows from the
results derived that the approximate Laughlin wavefunction for the fractional
Quantum Hall Effect satisfies the node coalescence condition. It is further
noted that the integral form makes evident that unlike the electron-nucleus
coalescence condition, the differential form of the electron-electron
coalescence condition cannot be expressed in terms of the electron density at
the point of coalescence. From the integral form, the integral and differential
coalescence conditions for the pair-correlation function in $D\geq 2$ dimension
space are also derived. The known differential form of the pair function cusp
condition for the uniform electron gas in dimensions $D = 2,3$ constitute a
special case of the result derived.
