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arXiv · 2601.10777

Summing series using recurrence relations

Erik Talvila
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Abstract

Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation yields a closed form for the series. This method is used to sum several series and to solve two {\it American Mathematical Monthly} problems.

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Erik Talvila. 2026-01-15. Summing series using recurrence relations. https://arxiv.org/abs/2601.10777

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