Recurrence relations for orthogonal polynomials on a triangle

Abstract

This paper derives sparse recurrence relations between orthogonal polynomials on a triangle and their partial derivatives, which are analogous to recurrence relations for Jacobi polynomials. We derive these recurrences in a systematic fashion by introducing ladder operators that map an orthogonal polynomial to another by incrementing or decrementing its associated parameters by one.

References in corpus (1)

• Tensor calculus in polar coordinates using Jacobi polynomials

Cited by in corpus (4)

• Computation of Power Law Equilibrium Measures on Balls of Arbitrary Dimension
• Tensor calculus in spherical coordinates using Jacobi polynomials. Part-I: Mathematical analysis and derivations
• A sparse spectral method for Volterra integral equations using orthogonal polynomials on the triangle
• Sparse spectral and p-finite element methods for partial differential equations on disk slices and trapeziums