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Summing series using recurrence relations

Published 15 Jan 2026 in math.GM | (2601.10777v1)

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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Authors (1)

  1. Erik Talvila 

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