Best approximation of alternating power series (Q1073288)

This paper contains results in which the author extends the work of Fiedler, Jurkat, and himself from series of the form \(\sum (-1)^ na_ n\) to series of the form \(\sum (-x)^ na_ n\) where \(\{a_ n\}\) is moment sequence and \(0<x<1\). We find the best \(L^ p\) approximation to the sum of the series for \(p=\infty,2,1\), specifically find the error in each case, calculate the actual terms of the matrices involved explicitly and find the Gaussian distributions of the matrices.