perform Koepf-Zeilberger's algorithm
KoepfZeilberger(T, n, k, En)
(m, l)-fold hypergeometric term in n and k
name; denote the shift operator with respect to n
For a specified (m, l)-fold hypergeometric term T⁡n,k in n and k, the KoepfZeilberger(T, n, k, En) command constructs for T⁡n,k a Z-pair L,G that consists of a linear difference operator with coefficients that are polynomials of n over the complex number field
and a function G⁡n,k such that
A function T⁡n,k is an (m, l)-fold hypergeometric term if T⁡n+m,kT⁡n,k and T⁡n,k+lT⁡n,k are rational functions of n and k.
The output from the KoepfZeilberger command is a list of two elements L,G representing the computed Z-pair L,G.
T ≔ binomial⁡2⁢n3,2⁢k
Zpair ≔ KoepfZeilberger⁡T,n,k,En
Note that since T is not a hypergeometric term in n, Zeilberger's algorithm is not applicable to T.
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.
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