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In this chapter, we show how generating functions can be used to solve recurrence relations. We first introduce the basic terminology and then give an example that illustrates the method for a particularly simple recurrence relation. We obtain a closed form for the coefficients of the Fibonacci sequence. Before generalizing this result, we review the partial fraction decomposition. We then show how to find closed-form solutions for linear homogeneous recurrence relations.

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Recurrence Relations

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  • 发表日期：

    2025年

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  • Andreas Klappenecker,
  • Hyunyoung Lee

摘要

In this chapter, we show how generating functions can be used to solve recurrence relations. We first introduce the basic terminology and then give an example that illustrates the method for a particularly simple recurrence relation. We obtain a closed form for the coefficients of the Fibonacci sequence. Before generalizing this result, we review the partial fraction decomposition. We then show how to find closed-form solutions for linear homogeneous recurrence relations.