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SumTools[IndefiniteSum]

  

AccurateSummation

  

compute closed forms of indefinite sums using accurate summation

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

AccurateSummation(T, n)

Parameters

T

-

function of n

n

-

name; specifies summation index

Description

• 

The AccurateSummation(T, n) command solves the problem of indefinite summation using accurate summation.

• 

The output from AccurateSummation is a function G such that Tn=Gn+1Gn if the algorithm succeeds in constructing one. Otherwise, it returns FAIL.

Examples

withSumTools[IndefiniteSum]:

TΓn+1ΓnΨn

T:=Γn+1ΓnΨn

(1)

AccurateSummationT,n

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

(2)

Note that since T is not a hypergeometric term of n, Gosper's algorithm fails to compute an anti-difference:

HypergeometricT,n

FAIL

(3)

References

  

Abramov, S.A. and van Hoeij, M. "Integration of Solutions of Linear Functional Equations." Integral Transformations and Special Functions, (1999): 3-12. Vol. 8. No. 1-2.

See Also

SumTools[IndefiniteSum]

SumTools[IndefiniteSum][Indefinite]

 


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