|
SumTools[Hypergeometric][ExtendedGosper] - perform extended Gosper's algorithm
|
|
Calling Sequence
|
|
ExtendedGosper(T, n)
|
|
|
Parameters
|
|
|
T
|
-
|
list or set of hypergeometric terms of n
|
|
n
|
-
|
variable
|
|
|
|
|
|
Description
|
|
|
•
|
Let En be the shift operator with respect to n, defined by  . For the given set (list)
|
, t[p](n), () .. ()}](/support/helpjp/helpview.aspx?si=5475/file06619/math59.png)
|
|
where the ](/support/helpjp/helpview.aspx?si=5475/file06619/math62.png) are hypergeometric terms of n, the ExtendedGosper(T,n) command returns a set (list)
|
, s[q](n), () .. ()}](/support/helpjp/helpview.aspx?si=5475/file06619/math72.png)
|
|
of hypergeometric terms ](/support/helpjp/helpview.aspx?si=5475/file06619/math75.png) such that
|
, i = 1 .. q)) = sum(t[j](n), j = 1 .. p)](/support/helpjp/helpview.aspx?si=5475/file06619/math81.png)
|
|
if each of the hypergeometric term ](/support/helpjp/helpview.aspx?si=5475/file06619/math84.png) exists. Otherwise, the ExtendedGosper routine returns the error message ``no solution found''.
|
|
|
|
Examples
|
|
|
>
|
![with(SumTools[Hypergeometric])](/support/helpjp/helpview.aspx?si=5475/file06619/math95.png)
|
|
>
|
|
|
| (1) |
|
>
|
|
|
| (2) |
|
>
|
![T := [n^2*4^n/((n+1)*(n+2)), 2^(2*n-1)/(n*(2*n+1)*binomial(2*n, n)), -n^2*4^n/((n+1)*(n+2))+(n+1)^2*4^(n+1)/((n+2)*(n+3))]](/support/helpjp/helpview.aspx?si=5475/file06619/math113.png)
|
|
![T := [n^2*4^n/((n+1)*(n+2)), 2^(2*n-1)/(n*(2*n+1)*binomial(2*n, n)), -n^2*4^n/((n+1)*(n+2))+(n+1)^2*4^(n+1)/((n+2)*(n+3))]](/support/helpjp/helpview.aspx?si=5475/file06619/math116.png)
| (3) |
|
>
|
|
|
![[(-2*n-1)*2^(2*n-1)/(n*(2*n+1)*binomial(2*n, n)), (1/3)*(n-1)*4^(n+1)/(n+2)]](/support/helpjp/helpview.aspx?si=5475/file06619/math123.png)
| (4) |
No solution found:
|
>
|
|
|
| (5) |
|
>
|
|
|
|
|
References
|
|
|
|
Petkovsek, M.; Wilf, H.; and Zeilberger, D. A=B. Wellesley, Massachusetts: A. K. Peters Ltd., 1996.
|
|
|
Download Help Document
Was this information helpful?
