The Gosper(T,n,r) command solves the problem of indefinite hypergeometric summation, that is, for the given hypergeometric term  of , it constructs another hypergeometric term  of  such that , provided that such a term exists. Otherwise, the function returns the error message "no solution found".

If the third optional argument  is specified, it is assigned the rational function  such that  if  was computed successfully, and FAIL otherwise.

Error, (in SumTools:-Hypergeometric:-Gosper) no solution found

Gosper, R.W., Jr. "Decision procedure for indefinite hypergeometric summation." Proc. Natl. Acad. Sci. USA. Vol. 75. (1977): 40-42.