Numerical comparison of abstract Pade-approximants and abstract rational approximants with other generalizations of the classical pade-approximant

1981 ◽  
pp. 137-157 ◽  
Author(s):  
Annie A. M. Cuyt
Keyword(s):  
Padé Approximants ◽  
Padé Approximant ◽  
Numerical Comparison ◽  
Rational Approximants ◽  
Pade Approximants ◽  
Pade Approximant

Padé Approximant Calculation of p-Wave π–π Scattering with a σ Model Lagrangian

1971 ◽  
Vol 49 (3) ◽  
pp. 360-366
Author(s):  
D. K. Elias
Keyword(s):  
Padé Approximants ◽  
Padé Approximant ◽  
P Wave ◽  
Pade Approximants ◽  
Pade Approximant ◽  
Wave Channel ◽  
Wave Resonance ◽  
Text Interaction ◽  
Range Of Values ◽  
D Wave

A π–π it interaction via a scalar I = 0, σ exchange is considered. The contribution of the t and u channel exchanges of the σ to the p-wave, I = 1 amplitude is calculated using Padé approximants. A p-wave resonance, interpreted as the p meson, the width of which depends on the mass of the input a meson, is found; for a certain range of values of the σ mass the ρ width compares not unfavorably with similar calculations using a [Formula: see text] interaction. However, for the range of masses considered the width is considerably smaller than the experimental value. The I = 0, d-wave channel is also considered and a resonance, interpreted as the ƒ0(1260), is found.

scholarly journals Probing the Infrared Structure of Gauge Theories: A Padé-Approximant Approach

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 913-915 ◽  
Author(s):  
F. A. Chishtie ◽  
V. Elias ◽  
V. A. Miransky ◽  
T. G. Steele
Keyword(s):  
Fixed Point ◽  
Gauge Theory ◽  
Gauge Theories ◽  
Padé Approximants ◽  
Padé Approximant ◽  
Pade Approximants ◽  
Pade Approximant ◽  
Specific Choice ◽  
Large N ◽  
Β Function

Padé-approximant treatments of the known terms of the QCD β-function are seen to develop possible infrared fixed point structure only if the number of fermion flavours is sufficiently large. This flavour threshold is seen to be between six and nine flavours, depending upon both the specific choice of approximant as well as on the presently-unknown five-loop β-function contribution. Below this flavour threshold, Padé approximants based upon the QCD β-function manifest the same infrared attractor structure as that which characterizes the exact NSVZ β-function of supersymmetric gluodynamics. Such infrared attractor structure is also seen to characterize Padé-approximant treatments of vector SU(N) gauge theory in the large N limit, suggesting common infrared dynamics for the strong and weak phases of this theory.

scholarly journals Two-dimensional generalized instantaneous images and approximations of the Pade type function of two variables

2020 ◽  
pp. 75-80
Author(s):  
I. Teteruk
Keyword(s):  
Exponential Function ◽  
Hypergeometric Series ◽  
Special Functions ◽  
Basic Hypergeometric Series ◽  
Padé Approximants ◽  
Two Dimensional ◽  
Rational Approximants ◽  
One Dimensional ◽  
Pade Approximants ◽  
Function Of Two Variables

Generalized instantaneous image were introduced by V.K. Dzyaduk [1] in 1981 and proved to be a convenient tool for constructing and studying the Padé approximants and their generalizations (see [2]). The method of generalized instantaneous images proposed by Dzyadyk made it possible to construct and study rational Padé approximants and their generalizations for many classes of special functions from a single position. As an example, the Padé approximants is constructed for a class of basic hypergeometric series, which includes a q-analogue of the exponential function. In this paper the construction of the Pade approximants for the function of two variables is investigated. A two-dimensional functional sequence is constructed, which has a generalized instantaneous image, and rational approximants are determined, which will be generalizations of one-dimensional Padé approximants. The function of the two variables is entirely related to the basic hypergeometric series.

Rational approximants defined from power series in N variables

1974 ◽  
Vol 336 (1607) ◽  
pp. 421-452 ◽  
Keyword(s):  
Power Series ◽  
Complex Variable ◽  
Padé Approximants ◽  
Theoretical Physics ◽  
Rational Approximants ◽  
Pade Approximants ◽  
Complex Variable Methods ◽  
Several Variables ◽  
Exclusive Sets

Rational approximants in N variables z r ( r = 1, 2, ..., N ) are defined from power series in these variables. They are generalizations of the two-variable approximants defined recently, and have the properties: ( i ) they possess symmetry between the N variables; ( ii ) they exist and are in general unique: ( iii ) if any k (< N ) variables are equated to zero, the approximants reduce to approximants in ( N — k ) variables formed from the corresponding reduced power series; in particular, if k = N — 1, they reduce to diagonal Padé approximants; ( iv ) their definition is invariant under the group of transformations z r = Aω r /(1 — B r ω r ) provided A ≠ 0, for all r = 1, 2, ..., N ; this group of homographic transformations preserves the origin z r = 0 ( r = 1, 2, ..., N ) but does not allow changes in the relative scales of the variables z r ; ( v ) an approximant formed from the reciprocal series is the reciprocal of the corresponding original approximant; ( vi ) if the series is the product of two power series in mutually exclusive sets of variables, the approximant is the product of the corresponding approximants formed from the two series; ( vii ) if the series is the sum of two power series in mutually exclusive sets of variables, the approximant is the sum of the corresponding approximants formed from the two series. Rigorous proofs of the properties ( i ) and ( iii ) to ( vii ) are given, based on complex variable methods. We discuss the possible use of the approximants in practical problems, especially in theoretical physics, and their possible importance in the theory of functions of several variables.

Phenomenological applications of rational approximants

2016 ◽  
Vol 31 (29) ◽  
pp. 1630028 ◽  
Author(s):  
Sergi Gonzàlez-Solís ◽  
Pere Masjuan
Keyword(s):  
Form Factor ◽  
Pseudoscalar Meson ◽  
Padé Approximants ◽  
Summation Method ◽  
Low Energy ◽  
Vector Form Factor ◽  
Vector Form ◽  
Rational Approximants ◽  
Pade Approximants

We illustrate the powerfulness of Padé approximants (PAs) as a summation method and explore one of their extensions, the so-called quadratic approximant (QAs), to access both space- and (low-energy) time-like (TL) regions. As an introductory and pedagogical exercise, the function [Formula: see text] is approximated by both kind of approximants. Then, PAs are applied to predict pseudoscalar meson Dalitz decays and to extract [Formula: see text] from the semileptonic [Formula: see text] decays. Finally, the [Formula: see text] vector form factor in the TL region is explored using QAs.

scholarly journals Padé approximants as limits of best rational approximants

1974 ◽  
Vol 12 (2) ◽  
pp. 201-204 ◽  
Author(s):  
Charles K Chui ◽  
Oved Shisha ◽  
Philip W Smith
Keyword(s):  
Padé Approximants ◽  
Rational Approximants ◽  
Pade Approximants ◽  
Best Rational Approximants
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