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Communications of the ACM

Communications of the ACM

A recurrence scheme for converting from one orthogonal expansion into another

A generalization of a scheme of Hamming for converting a polynomial Pn(x) into a Chebyshev series is combined with a recurrence scheme of Clenshaw for summing any finite series whose terms satisfy a three-term recurrence formula. An application to any two orthogonal expansions Pn(x) = ∑nm=0 amqm(x) = ∑nm=0 AmQm(x) enables one to obtain Am directly from am, m = 0(1)n, by a five-term recurrence scheme.

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