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#<math display="inline">\gcd ( b(n), c(n+1))=1</math>.
This representation of <math display="inline">r(n)</math> is called Gosper-Petkovšek normal form. These polynomials can be computed explicitly. This construction of the representation is an essential part of [[Gosper's algorithm]].<ref>{{Cite journal |last=Gosper |first=R. William |date=1978 |title=Decision procedure for indefinite hypergeometric summation |url=https://pdfs.semanticscholar.org/c66e/0beca13f866f748971d18bd39ebdc2b88751.pdf |archive-url=https://web.archive.org/web/20180727145550/https://pdfs.semanticscholar.org/c66e/0beca13f866f748971d18bd39ebdc2b88751.pdf |url-status=dead |archive-date=2018-07-27 |journal=[[Proc. Natl. Acad. Sci. USA]] |volume=75 |issue=1 |pages=40–42|doi=10.1073/pnas.75.1.40 |pmid=16592483 |pmc=411178 }}</ref> Petkovšek added the conditions 2. and 3. of this representation which makes this normal form unique.<ref name=":0" />
== Algorithm ==
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