What question did this study set out to answer?

The aim is to develop a unified stochastic approach for Taylor-type expansions using independent random variables.

February 20, 2026MathematicsOpen Access

Probabilistic Taylor-Type Expansions of Functions

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Investigates a probabilistic framework for Taylor-type expansions, suggesting enhanced guidelines for approximation methods.

The aim is to develop a unified stochastic approach for Taylor-type expansions using independent random variables.
Investigated Taylor–Young and Maclaurin series for smooth function approximations.
Introduced probabilistic expansions incorporating evaluations of derivatives at multiple points.
Analyzed the effect of different random variable distributions on expansions, especially under truncation.
Exact expansions for any order of available derivatives were achieved.
Traditional Taylor and Maclaurin series are shown to be specific cases of this new approach.
Enhanced guidelines for choosing optimal distributions for random variables in expansions were developed.

Matieyendou Lamboni (2026) studied this question.

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