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Mathematics LibreTexts

4.3: Generating Functions and Recurrence Relations

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Recall that a recurrence relation for a sequence \(a_{n}\) expresses \(a_{n}\) in terms of values \(a_{i}\) for \(i < n\). For example, the equation \(a_{i} = 3a_{i}−1+2^{i}\) is a first order linear constant coefficient recurrence.

4.3.1 How Generating Functions are Relevant

Algebraic manipulations with generating functions can sometimes reveal the
solutions to a recurrence relation.