Work

A complete asymptotic expansion for the semi-exponential operators related to $$x^{3}$$

Year: 2026

Type: article

Abstract: In the present paper, we study the asymptotic properties of the semi-exponential operator connected with $$p\left( x\right) =x^{3}$$ p x = x 3 . The main result is a pointwise complete asymptotic expansion valid for locally smooth functions of exponential growth. All coefficients are derived and explicitly given. Furthermore, we characterize classes of functions f for which the semi-exponential operator connected with $$p\left( x\right) =x^{3}$$ p x = x 3 provides asymptotically a better approximation than the corresponding operator of exponential type. Finally, we present numerical examples which illustrate the better rate of convergence.

Source: Computational and Applied Mathematics

DOI: 10.1007/s40314-026-03688-3

Authors: Ulrich Abel, Vijay Gupta, Vitaliy Kushnirevych

Institutions: Technische Hochschule Mittelhessen, Netaji Subhas University of Technology

Language: English

Topic: Approximation Theory and Sequence Spaces

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,390

OpenAlex ID: W7160836334