Riemann–Liouville fractional integration and reduced distributions on hyperspheres Kingsley R. W. Jones School of Physics, University of Melbourne, Parkville 3052, Melbourne, Australia. (Revised Version) January 5, 1991 Abstract Using properties of Dirichlet’s iterated integral formula we show how the Riemann-Liouville fractional integral unifies arbitrary mo- ment calculations for reduced distributions on hyperspheres. A whole class of problems of this type are then reduced to readily identifiable integral transforms. The work is applied to quantum inference and connections made to random matrix theory aspects of nuclear physics and quantum chaos. Short title: Fractional integration and hyperspherical moments PACS: 1