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QDifferenceEquations

  

Zeilberger

  

perform Zeilberger's algorithm (q-difference case)

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

Zeilberger(T, n, k, q, Qn)

Parameters

T

-

q-hypergeometric term in  and

n

-

name

k

-

name

q

-

name

Qn

-

name; denote the q-shift operator with respect to

Description

• 

For a specified q-hypergeometric term  of  and , the Zeilberger(T, n, k, q, Qn) calling sequence constructs for  a Z-pair  that consists of a linear q-difference operator with coefficients that are polynomials of

  

and a q-hypergeometric term  of  and  such that

• 

Qn is the q-shift operator with respect to , defined by .

• 

By assigning values to the global variables _MINORDER and _MAXORDER, the algorithm is restricted to finding a Z-pair  for  such that the order of L is between _MINORDER and _MAXORDER (the default value of _MAXORDER is 6).

• 

The output from the Zeilberger command is a list of two elements  representing the computed Z-pair .

Examples

(1)

(2)

(3)

(4)

(5)

(6)

References

  

Petkovsek, M.; Wilf, H.; and Zeilberger, D. A=B. Wellesley, Massachusetts: A K Peters, Ltd., 1996.

See Also

SumTools[Hypergeometric][Zeilberger]

 


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