Reconstructing Generalized Exponential Laws by Self-Similar Exponential Approximants

TL;DR

This paper introduces a method using self-similar exponential approximants to accurately reconstruct quasi-exponential functions from limited series data, outperforming traditional Padé approximants.

Contribution

The paper presents a novel application of self-similar exponential approximants for reconstructing exponential laws, demonstrating superior accuracy over Padé approximants.

Findings

Self-similar exponential approximants outperform Padé approximants in reconstruction accuracy.

The method effectively reconstructs functions from limited power series terms.

Significant improvement in functional approximation quality is achieved.

Abstract

We apply the technique of self-similar exponential approximants based on successive truncations of continued exponentials to reconstruct functional laws of the quasi-exponential class from the knowledge of only a few terms of their power series. Comparison with the standard Pad\'e approximants shows that, in general, the self-similar exponential approximants provide significantly better reconstructions.