“Know how to solve every problem that has been solved.” “What I cannot create, I do not understand.” — Richard Feynman

Classical orthogonal polynomials are calculated in numerical contexts with their three-term recurrence relation, not explicit formulas — the latter suffer catastrophic cancellation at high degree.

Claims

Classical orthogonal polynomials are calculated in numerical contexts with their three-term recurrence relation, not explicit formulas — the latter suffer catastrophic cancellation at high degree.

✓ supported computational 90% stub numerical-methodsorthogonal-polynomialsnumerical-stabilityspecial-functions

Connections

generalizes chebyshev-nodes-avoid-runges-phenomenon

Referenced by

instance-of Interpolating at Chebyshev nodes avoids Runge's phenomenon, which afflicts polynomial interpolation at equispaced points.