I ran across an interesting footnote in Wolfram Koepf’s book *Computer Algebra*.

Gosper’s algorithm [1] was probably the first algorithm which would not have been found without computer algebra. Gosper writes in his paper: “Without the support of MACSYMA and its developer, I could not have collected the experiences necessary to provoke the conjectures that lead to the algorithm.”

When I first glanced at the footnote I misread it, coming away with the impression that Gosper said he could not have proved that his algorithm was correct without computer algebra. But he said he would not have *formulated* his algorithm without his experience using MACSYMA.

If a sum of hypergeometric terms is itself hypergeometric, Gosper’s algorithm gives a way to find the sum. Gosper’s algorithm, discovered using computer algebra, is itself an important computer algebra algorithm.

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[1] Koepf cites Gosper as R. W. Gosper, Jr. Decision procedure for indefinite hypergeometric summation. *Proc*. *Natl*. *Acad*. *Sci*. USA, 75, 1978, 40–42.