# Two-point quasifractional approximant in physics. Truncation error

## Abstract

The quasifractional approximation method is developed in a systematic manner. This method uses simultaneously the power series, and at a second point, the asymptotic expansion. The usual form of the approximants is two or more rational fractions, in terms of a suitable variable, combined with auxiliary nonfractional functions. Coincidence in the singularities in the region of interest is pursued. Equal denominators in the rational fractions is required so that the solution of only linear algebraic equations is needed to determine the parameters of the approximant. An upper bound is obtained for the truncation error for a certain class of functions, which contains most of the functions for which this method has been applied so far. It is shown that quasifractional approximants can be derived as a mixed German and Latin polynomial problem in the context of Hermite--Pade approximation theory.

- Authors:

- (Deptomento de Fisica, Universidad Simon Bolivar, Apartado 89000, Caracas, Venezuela (VE))
- (Theoretical Division, Los Alamos National Laboratory, University of California, Los Alamos, New Mexico 87545 (USA))

- Publication Date:

- OSTI Identifier:
- 5661731

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Physics (New York); (USA)

- Additional Journal Information:
- Journal Volume: 32:6; Journal ID: ISSN 0022-2488

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; NUMERICAL ANALYSIS; FUNCTIONS; PADE APPROXIMATION; ERRORS; BESSEL FUNCTIONS; BORN APPROXIMATION; PHYSICS; POWER SERIES; QUANTUM FIELD THEORY; SERIES EXPANSION; SINGULARITY; WKB APPROXIMATION; FIELD THEORIES; MATHEMATICS; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

### Citation Formats

```
Martin, P., and Baker, G.A. Jr.
```*Two-point quasifractional approximant in physics. Truncation error*. United States: N. p., 1991.
Web. doi:10.1063/1.529304.

```
Martin, P., & Baker, G.A. Jr.
```*Two-point quasifractional approximant in physics. Truncation error*. United States. doi:10.1063/1.529304.

```
Martin, P., and Baker, G.A. Jr. Sat .
"Two-point quasifractional approximant in physics. Truncation error". United States. doi:10.1063/1.529304.
```

```
@article{osti_5661731,
```

title = {Two-point quasifractional approximant in physics. Truncation error},

author = {Martin, P. and Baker, G.A. Jr.},

abstractNote = {The quasifractional approximation method is developed in a systematic manner. This method uses simultaneously the power series, and at a second point, the asymptotic expansion. The usual form of the approximants is two or more rational fractions, in terms of a suitable variable, combined with auxiliary nonfractional functions. Coincidence in the singularities in the region of interest is pursued. Equal denominators in the rational fractions is required so that the solution of only linear algebraic equations is needed to determine the parameters of the approximant. An upper bound is obtained for the truncation error for a certain class of functions, which contains most of the functions for which this method has been applied so far. It is shown that quasifractional approximants can be derived as a mixed German and Latin polynomial problem in the context of Hermite--Pade approximation theory.},

doi = {10.1063/1.529304},

journal = {Journal of Mathematical Physics (New York); (USA)},

issn = {0022-2488},

number = ,

volume = 32:6,

place = {United States},

year = {1991},

month = {6}

}