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arXiv · 2609.06152

The Levin Method for the Summation of One-dimensional and Multidimensional Infinite Series

David Levin
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Abstract

The Levin method transforms the evaluation of a highly oscillatory integral into the solution of a first-order linear ODE for a slowly varying auxiliary function. This ODE is typically approximated by collocation, after which the integral value is recovered from the auxiliary function at the endpoints. The present work develops a new extension of the Levin method for the summation of one-dimensional and multidimensional infinite oscillatory series. The summation problem is transformed into the solution of a functional equation involving transformed arguments of the unknown function. The resulting approach is particularly attractive in the multidimensional setting, where the range of existing numerical methods is relatively limited.

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David Levin. 2026-09-05. The Levin Method for the Summation of One-dimensional and Multidimensional Infinite Series. https://arxiv.org/abs/2609.06152

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