Multiseries approximants

Phase Transition and Padé Approximants for Fröhlich Polarons

“…[n/n] and [n, -l/n] give us upper and lower bounds, respectively [5]. This fact is connected with the bounding properties of multipoint Pad6 approximants, studied by Barnsley [ 7 ] .…”

Extending the quasi-steady state approximation by changing variables

“…(This step is not essential to our main line of argument.) Such an expression is provided by a two-point Pad6 approximant (Baker and Graves-Morris, 1984). The lowest order Pad6 approximant consists of the quotient of two linear functions of 5.…”

Analytical Construction of Homoclinic Orbits of Two- And Three-Dimensional Dynamical Systems

“…In order to join local expansions, fractional rational diagonal two-point Pade' approximants (PA) [11] can be used. Assume that there are local expansions obtained at small and large values of a parameter c (for example, the parameter is an amplitude value of the periodic solution) [9,10,12].…”

“…One utilizes the potentiality condition (11). Substituting expansion (16) into equation (11) and integrating, one has…”