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Accelerating Convergence in Series and Infinite Integrals: Revisiting Levin and Sidi's Contributions (2508.01406v1)
Published 2 Aug 2025 in math.NA and cs.NA
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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