SumTools[Hypergeometric]
Gosper
perform indefinite hypergeometric summation
Calling Sequence
Parameters
Description
Examples
References
Gosper(T, n, r)
T
-
hypergeometric term of n
n
variable
r
(optional) name
The Gosper(T,n,r) command solves the problem of indefinite hypergeometric summation, that is, for the given hypergeometric term T of n, it constructs another hypergeometric term G of n such that Tn=Gn+1−Gn, provided that such a term exists. Otherwise, the function returns the error message "no solution found".
If the third optional argument r is specified, it is assigned the rational function rn such that Gn=rnTn if G was computed successfully, and FAIL otherwise.
withSumToolsHypergeometric:
T≔4nn4binomial2n,n
T≔4nn42nn
GosperT,n
2n−163n4−140n3+60n2+26n−64n6932nn
T≔Productj3,j=1..n−1Productj3+1,j=1..n
T≔∏j=1n−1j3∏j=1nj3+1
GosperT,n,r
n+1I3−2n+1I3+2n−1∏j=1n−1j34∏j=1nj3+1
n+1I3−2n+1I3+2n−14
No hypergeometric solution found:
T≔n2binomial2n,n
T≔n22nn
Error, (in SumTools:-Hypergeometric:-Gosper) no solution found
FAIL
Gosper, R.W., Jr. "Decision procedure for indefinite hypergeometric summation." Proc. Natl. Acad. Sci. USA. Vol. 75. (1977): 40-42.
See Also
SumTools[Hypergeometric][ExtendedGosper]
SumTools[Hypergeometric][PolynomialNormalForm]
SumTools[Hypergeometric][SumDecomposition]
SumTools[Hypergeometric][Zeilberger]
SumTools[IndefiniteSum][AccurateSummation]
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