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arXiv · 2508.01406

Accelerating Convergence in Series and Infinite Integrals: Revisiting Levin and Sidi's Contributions

David Levin
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Abstract

The evaluation of slowly converging series and infinite integrals is a key challenge in numerical analysis and computational mathematics. In their influential 1981 paper, the author and Avram Sidi introduced two effective nonlinear transformations, the d-transformation for series and the D-transformation for infinite integrals, aimed at speeding up their convergence. This review summarizes, contextualizes, and evaluates their contributions, highlighting the mathematical basis, practical significance, and legacy of their work.

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David Levin. 2025-08-02. Accelerating Convergence in Series and Infinite Integrals: Revisiting Levin and Sidi's Contributions. https://arxiv.org/abs/2508.01406

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