  A formula for evaluating the quadratic normalization integrals of orthogonal
Heun functions over the real interval 0 <= x <= 1 is derived using a simple
limiting procedure based upon the associated differential equation. The
resulting expression gives the value of the normalization integral explicitly
in terms of the local power-series solutions about x=0 and x=1 and their
derivatives. This provides an extremely efficient alternative to numerical
integration for the development of an orthonormal basis using Heun functions,
because all of the required information is available as a by-product of the
search for the eigenvalues of the differential equation.
  02.30.Gp; 02.30.Hq; 02.70.-c; 02.60.Jh
