Ramanujanʼs Master Theorem for Riemannian symmetric spaces

Ramanujanʼs Master Theorem states that, under suitable conditions, the Mellin transform of a power series provides an interpolation formula for the coefficients of this series. Based on the duality of compact and noncompact reductive Riemannian symmetric spaces inside a common complexification, we prove an analogue of Ramanujanʼs Master Theorem for the spherical Fourier transform of a spherical Fourier series. This extends the results proven by Bertram for Riemannian symmetric spaces of rank-one.