# Criteria for the Application of Double Exponential Transformation

## TL;DR

This paper explores the use of double exponential transformations for calculating improper integrals, demonstrating their superior accuracy over single exponential methods and discussing applications in Fourier integrals.

## Contribution

It introduces improved integral estimates using double exponential transformation and compares its error margins with single exponential methods.

## Key findings

- Double exponential transformation reduces error margins in improper integral calculations.
- Double exponential methods outperform single exponential methods in accuracy.
- Application of double exponential transformation in Fourier integrals is discussed.

## Abstract

The double exponential formula was introduced for calculating definite integrals with singular point oscillation functions and Fourier-integrals. The double exponential transformation is not only useful for numerical computations but it is also used in different methods of Sinc theory. In this paper we use double exponential transformation for calculating particular improper integrals. By improving integral estimates having singular final points. By comparison between double exponential transformations and single exponential transformations it is proved that the error margin of double exponential transformations is smaller. Finally Fourier-integral and double exponential transformations are discussed.