  Ramanujan's Master theorem states that, under suitable conditions, the Mellin
transform of an alternating power series provides an interpolation formula for
the coefficients of this series. Ramanujan applied this theorem to compute
several definite integrals and power series, which explains why it is referred
to as the "Master Theorem". In this paper we prove an analogue of Ramanujan's
Master theorem for the hypergeometric Fourier transform on root systems. This
theorem generalizes to arbitrary positive multiplicity functions the results
previously proven by the same authors for the spherical Fourier transform on
semisimple Riemannian symmetric spaces.
