|
SumTools[Hypergeometric][KoepfZeilberger] - perform Koepf-Zeilberger's algorithm
|
|
Calling Sequence
|
|
KoepfZeilberger(T, n, k, En)
|
|
|
Parameters
|
|
|
T
|
-
|
(m, l)-fold hypergeometric term in n and k
|
|
n
|
-
|
name
|
|
k
|
-
|
name
|
|
En
|
-
|
name; denote the shift operator with respect to n
|
|
|
|
|
|
Description
|
|
*En^v+`...`+a[1](n)*En+a[0](n)](/support/helpjp/helpview.aspx?si=5480/file06627/math94.png)
|
|
and a function  such that
|
|
•
|
The output from the KoepfZeilberger command is a list of two elements ![[L, G]](/support/helpjp/helpview.aspx?si=5480/file06627/math120.png) representing the computed Z-pair  .
|
|
|
|
Examples
|
|
|
>
|
![with(SumTools[Hypergeometric])](/support/helpjp/helpview.aspx?si=5480/file06627/math131.png)
|
|
>
|
|
|
| (1) |
|
>
|
|
|
![Zpair := [-4+En^3, 6*(-(1/2)*n-1+k)*k*(2*k-1)*binomial((2/3)*n, 2*k)/((-(1/3)*n+k-1)*(-(2/3)*n+2*k-1)*n)]](/support/helpjp/helpview.aspx?si=5480/file06627/math145.png)
| (2) |
|
>
|
|
|
| (3) |
|
>
|
|
|
| (4) |
Note that since T is not a hypergeometric term in n, Zeilberger's algorithm is not applicable to T.
|
|
|
References
|
|
|
|
Koepf, W. "Algorithms for m-fold Hypergeometric Summation." Journal of Symbolic Computation. Vol. 20 No. 4. (1995): 399-417.
|
|
|
Koepf, W. Hypergeometric Summation: An Algorithmic Approach to Summation and Special Function Identities. Braunschweig, Germany: Vieweg, 1998.
|
|
|
Download Help Document
Was this information helpful?
