  The problem of extrapolating the series in powers of small variables to the
region of large variables is addressed. Such a problem is typical of quantum
theory and statistical physics. A method of extrapolation is developed based on
self-similar factor and root approximants, suggested earlier by the authors. It
is shown that these approximants and their combinations can effectively
extrapolate power series to the region of large variables, even up to infinity.
Several examples from quantum and statistical mechanics are analysed,
illustrating the approach.
