A simple algorithm for the evaluation of the hypergeometric series using quasi-linear time and linear space

TL;DR

This paper introduces a straightforward algorithm that efficiently evaluates hypergeometric series with rational coefficients, achieving quasi-linear time and linear space complexity, useful for practical computational applications involving mathematical constants.

Contribution

The paper presents a novel, simple algorithm for hypergeometric series evaluation with improved computational complexity and practical applicability.

Findings

Algorithm operates in quasi-linear time.

Uses linear space complexity.

Suitable for computing mathematical constants.

Abstract

A simple algorithm with quasi-linear time complexity and linear space complexity for the evaluation of the hypergeometric series with rational coefficients is constructed. It is shown that this algorithm is suitable in practical informatics for constructive analogues of often used constants of analysis.