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SumTools[Hypergeometric][IndefiniteSum] - calculate indefinite sum

Calling Sequence

IndefiniteSum(T, n)

Parameters

T

-

function of n

n

-

variable

Description

• 

The IndefiniteSum(T,n) command computes a function G such that Tn=En1.Gn if it exists.

• 

The classes of functions T supported are rational functions, hypergeometric terms, and those for which the minimal annihilator in KnEn for T can be computed.

Examples

withSumTools[Hypergeometric]:

T:=1n2+5n1

T:=1n2+5n1

(1)

nT=IndefiniteSumT,n

n1n2+5n1=13n32+12513n12+12513n+12+125

(2)

T:=n32n

T:=n32n

(3)

nT=IndefiniteSumT,n

nn32n=n36n2+18n262n

(4)

T:=Γn+1ΓnΨn

T:=Γn+1ΓnΨn

(5)

nT=IndefiniteSumT,n

nΓn+1ΓnΨn=n4n36n26n5Γn+1ΓnΨnn2+n+3n5n410n39n22Γn+2Γn+1Ψn+1nn2+n+3+n+1n35n2+4n2Γn+3Γn+2Ψn+2nn2+n+3

(6)

See Also

sum, SumTools[Hypergeometric], SumTools[Hypergeometric][DefiniteSum], SumTools[Hypergeometric][Gosper], SumTools[Hypergeometric][SumDecomposition], SumTools[IndefiniteSum][AccurateSummation]

References

  

Abramov, S.A. "Indefinite sums of rational functions." Proc. ISSAC'95, pp. 303-308. 1995.

  

Abramov, S.A., and van Hoeij, M. "Integration of solutions of linear functional equations." Integral Transformations and Special Functions, Vol. 8 No. 1-2, (1999): 3-12.

  

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


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