Abstract
Lanczos (1952) claims that expansion of a function in a series of Chebyshev polynomials is usually superior to expansion in a series of ultraspherical polynomials for any possible non-zero value of the parameter α. We look for conditions on the function under which this superiority can be proved and measured; we achieve some success on the assumption that α is positive, but the results for negative α are less satisfactory.
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