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How do the weighting functions for, eg, Chenyshev Type I polynomials influence their behavior?
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There are about dozen or so basis sets for orthogonal polynomials that Iām aware of. The primary distinguishing features appear to be the domain of orthogonality and the weighting function used inside the inner product definition. What drove the choices of those weights? How did they make these families of polynomials useful for some tasks and less so for others?
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