Summing series using recurrence relations
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.
Fields of Study & Subjects
Advanced Mathematical Identities
Mathematical functions and polynomials
Mathematical and Computational Methods
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 15 January 2026
- Document type
- Preprint