The practical use of the Euler transformation (Q1120946)

It is known that the generalized Euler transformation is one of the classical transformations of infinite series which can be used for the acceleration of convergence. If we apply this transformation to one series with rounded coefficients then its behaviour can differ from that predicted, theoretically. In this case, the author explains that it is possible to use this transformation for acceleration of convergence, but some changes are necessary in the method of choosing the optimum parameter value. This is shown with an illustrative example of a series solution of a linear differential equation.