Abstract
In this paper we describe a new family of polynomials which are eigenfunctions of a singular Sturm–Liouville problem on the triangle T 2 = { ( x , y ) : x ≥ 0 , y ≥ 0 , x + y 1 } . The polynomials are shown to be orthogonal over T 2 with respect to a unit weight function, and may be used in approximations which are exponentially convergent for functions which are infinitely smooth in T 2 . The zeros of the polynomials may be used in cubature formulae on T 2 .
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Schedule a callMore From: Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences
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