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SumTools[Hypergeometric][WZMethod] - perform Wilf-Zeilberger's algorithm
Calling Sequence
WZMethod(f,r,n,k,cert)
Parameters
f
-
function of n and k
r
function of n
n
variable
k
cert
(optional) name; assigned the computed WZ certificate
Description
The WZMethod(f,r,n,k,cert) command certifies identities of the form .
Let if and , otherwise. If the method succeeds in certifying the given identity, the output is a list of two elements representing the WZ-pair such that . Otherwise, it returns the error message "WZ method fails".
If the method is successful and if the fifth optional argument cert is given, cert is assigned the WZ certificate .
It is assumed that for each integer , and .
Examples
Proof of Gauss's 2F1 identity:
Proof of Dixon's identity:
See Also
limit, Sum, SumTools[Hypergeometric], SumTools[Hypergeometric][Gosper]
References
Wilf, H., and Zeilberger, D. "Rational function certify combinatorial identities." J. Amer. Math. Soc. Vol. 3. (1990): 147-158.
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