perform indefinite hypergeometric summation - Maple Help

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SumTools[Hypergeometric][Gosper] - perform indefinite hypergeometric summation

Calling Sequence

Gosper(T, n, r)

Parameters

T

-

hypergeometric term of n

n

-

variable

r

-

(optional) name

Description

• 

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+1Gn, 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.

Examples

withSumTools[Hypergeometric]:

T:=4nn4binomial2n,n

T:=4nn4binomial2n,n

(1)

GosperT,n

16932n163n4140n3+60n2+26n64nbinomial2n,n

(2)

T:=j=1n1j3j=1nj3+1

T:=j=1n1j3j=1nj3+1

(3)

GosperT,n,'r'

14I32n+1n+1I3+2n1j=1n1j3j=1nj3+1

(4)

r

14I32n+1n+1I3+2n1

(5)

No hypergeometric solution found:

T:=n2binomial2n,n

T:=n2binomial2n,n

(6)

GosperT,n,'r'

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

r

FAIL

(7)

See Also

SumTools[Hypergeometric], SumTools[Hypergeometric][ExtendedGosper], SumTools[Hypergeometric][PolynomialNormalForm], SumTools[Hypergeometric][SumDecomposition], SumTools[Hypergeometric][Zeilberger], SumTools[IndefiniteSum][AccurateSummation]

References

  

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


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