Work

On the Fourier transforms of rational, trigonometric, and inverse trigonometric functions

Year: 2026

Type: article

Abstract: In this paper, we derive the Fourier transforms of arbitrary rational functions in the sense of distributions by means of Jordan's lemma and contour integration. In addition, we obtain the Fourier transforms of all trigonometric functions in the sense of distributions, and the pointwise Fourier transforms of all inverse trigonometric functions.

Source: Integral Transforms and Special Functions

DOI: 10.1080/10652469.2026.2746505

Authors: Lingxin Zhu, Jie Wang, Baode Li

Institution: Xinjiang University

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Funder: National Natural Science Foundation of China

Award: G2738259490