  Using Darling's theorem on products of generalized hypergeometric series an
analytic expression is obtained for the Coulomb matrix elements in the lowest
Landau level in the representation of angular momentum. The result is important
in the studies of Fractional Quantum Hall effect (FQHE) in disk geometry.
Matrix elements are expressed as simple finite sums of positive terms,
eliminating the need to approximate these quantities with slowly-convergent
series. As a by-product, an analytic representation for certain integals of
products of Laguerre polynomials is obtained.
