%0 Journal Article
%A Owens, R. G.
%T Spectral approximations on the triangle
%D 1998
%R 10.1098/rspa.1998.0189
%J Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
%P 857-872
%V 454
%N 1971
%X In this paper we describe a new family of polynomials which are eigenfunctions of a singular Sturm–Liouville problem on the triangle T2={(x,y):x≥0,y≥0,x+y1}. The polynomials are shown to be orthogonal over T2 with respect to a unit weight function, and may be used in approximations which are exponentially convergent for functions which are infinitely smooth in T2. The zeros of the polynomials may be used in cubature formulae on T2.
%U http://rspa.royalsocietypublishing.org/content/royprsa/454/1971/857.full.pdf