@Article{Kirby:2009:SEC,
  author =       "R. Kirby",
  title =        "Singularity-free Evaluation of Collapsed-coordinate Orthogonal
                  Polynomials",
  journal =      "{ACM} Transactions on Mathematical Software",
  volume =       "37",
  number =       "1",
  accepted =     "5 June 2009",
  upcoming =     "true", 
  abstract =     "
                  The \( L^2 \)-orthogonal polynomials used in finite and
                  spectral element methods on nonrectangular elements may
                  be defined in terms of \emph{collapsed} coordinates,
                  wherein the shapes are mapped to a square or cube by
                  means of a singular change of variables. The orthogonal
                  basis is a product of specific Jacobi polynomials
                  in these new coordinates.  Implementations of these
                  polynomials require special handling of the coordinate
                  singularities. We derive new recurrence relations
                  for these polynomials on triangles and tetrahedra
                  that work directly in the original coordinates. These
                  relations, also applicable to pyramids and prisms, do
                  not require any special treatment of singular points.
                  These recurrences are seen to speed up both symbolic
                  and numerical computation of the orthogonal polynomials.",
}