  We give a new proof of the Macdonald-Mehta-Opdam integral identity for finite
Coxeter groups. This identity was conjectured by Macdonald and proved by Opdam
in 1993 using the theory of multivariable Bessel functions, but in
non-crystallographic cases the proof relied on a computer calculation by F.
Garvan. Our proof is somewhat more elementary (in particular, it does not use
multivariable Bessel functions), and uniform (does not refer to the
classification of finite Coxeter groups and does not use computers).
