A Comparison Between Chebyshev and Ultraspherical Expansions

This paper examines the norms of the projections from C–1,1] to P_M–1, 1] which are obtained by truncating Chebyshevand ultraspherical expansions after n terms. The norms are evaluatednumerically for n = 1, 2, 3 , ... , 10 and –0.1 5 wherethe ultraspherical weight function is (1 – x²)^x–.In particular the data show that the norm of the Chebyshev projectionis not the smallest in this range for 1 n 10.