# Algorithm for computing semi-Fourier sequences of expressions involving exponentiations and integrations

## TL;DR

This paper introduces an algorithm to compute semi-Fourier sequences for complex expressions involving arithmetic, exponentiation, and integration, extending the classical Fourier sequence concept beyond polynomials.

## Contribution

The paper presents the first algorithm for semi-Fourier sequences applicable to a broad class of expressions including exponentiation and integration.

## Key findings

- Algorithm successfully computes semi-Fourier sequences for complex expressions.
- Extends Fourier sequence concepts to non-polynomial expressions.
- Provides a foundation for further symbolic computation research.

## Abstract

We provide an algorithm for computing semi-Fourier sequences for expressions constructed from arithmetic operations, exponentiations and integrations. The semi-Fourier sequence is a relaxed version of Fourier sequence for polynomials (expressions made of additions and multiplications).