Acceleration of some logarithmic sequences

AbstractDelahaye and Germain-Bonne (1982) proved that the set of logarithmic sequences (LOG) is not accelerable. Nevertheless, some subsets of LOG can be accelerated. Most of the algorithms are based on the asymptotic expansion of the sequence to be accelerated. In this paper the point of view is quite different, since an analytic property of the whole sequence is used.If (Cn)nϵN is a sequence of moments with an integral representation in the interval [0, 1], then we w prove that the (Jacobi) modified moments accelerate (Cn)nϵN'' (Section 2). In a particular case (Section 3) the modified sequence can be written as a moment sequence, and a second modified sequence is formed, leading to further acceleration. The modified moments methods are particular summation processes using orthogonal polynomials which have been extensively studied by Wimp (1974, 1981)