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{{Short description|Summation method for hypergeometric terms}}
{{Use dmy dates|date=January 2020|cs1-dates=y}}
In [[mathematics]], '''Gosper's algorithm''', due to [[Bill Gosper]], is a procedure for finding sums of [[Hypergeometric identities|hypergeometric terms]] that are themselves hypergeometric terms. That is: suppose one has ''a''(1) + ... + ''a''(''n'') = ''S''(''n'') − ''S''(0), where ''S''(''n'') is a hypergeometric term (i.e., ''S''(''n'' + 1)/''S''(''n'') is a [[rational function]] of ''n''); then necessarily ''a''(''n'') is itself a hypergeometric term, and given the formula for ''a''(''n'') Gosper's algorithm finds that for ''S''(''n'').
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