Approximation with discrete projective transformation

Summation of power series by self-similar factor approximants

“…The direct application of Padé approximants [1] or their variants [33][34][35] does not allow for a correct description of critical indices. But the factor forms, analogous to approximants (5), should provide an accurate account of typical thermodynamic characteristics in the vicinity of critical points [36].…”

“…The self-similar factor approximants (5) look very appropriate for describing critical phenomena, where various thermodynamic functions usually possess power-law behaviour. The direct application of Padé approximants [1] or their variants [33][34][35] does not allow for a correct description of critical indices. But the factor forms, analogous to approximants (5), should provide an accurate account of typical thermodynamic characteristics in the vicinity of critical points [36].…”