On the Uniform Convergence of Generalized Fourier Series
- 1 June 1978
- journal article
- Published by Oxford University Press (OUP) in IMA Journal of Applied Mathematics
- Vol. 21 (4) , 379-386
- https://doi.org/10.1093/imamat/21.4.379
Abstract
We consider the convergence in the Chebychev norm of an expansion of a function of a real variable in terms of the classical orthogonal polynomials. Particular attention is paid to Fourier-Jacobi series and to the claim of Lanczos (1952) that expansion of a function in a series of Chebychev polynomials is usually superior to expansion in a series of Ultraspherical polynomials, Pn(λ)(x), for any non-zero value of λ.Keywords
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