  For the rational Baker-Akhiezer functions associated with special
arrangements of hyperplanes with multiplicities we establish an integral
identity, which may be viewed as a generalisation of the self-duality property
of the usual Gaussian function with respect to the Fourier transformation. We
show that the value of properly normalised Baker-Akhiezer function at the
origin can be given by an integral of Macdonald-Mehta type and explicitly
compute these integrals for all known Baker-Akhiezer arrangements. We use the
Dotsenko-Fateev integrals to extend this calculation to all deformed root
systems, related to the non-exceptional basic classical Lie superalgebras.
