|
SumTools[IndefiniteSum][AccurateSummation] - compute closed forms of indefinite sums using accurate summation
|
|
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  such that  if the algorithm succeeds in constructing one. Otherwise, it returns FAIL.
|
|
|
|
Examples
|
|
|
>
|
![with(SumTools[IndefiniteSum])](/support/helpjp/helpview.aspx?si=5459/file06638/math68.png)
|
|
>
|
|
|
| (1) |
|
>
|
|
|
| (2) |
Note that since T is not a hypergeometric term of n, Gosper's algorithm fails to compute an anti-difference:
|
>
|
|
|
| (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.
|
|
|
Download Help Document
Was this information helpful?
