perform Zeilberger's algorithm (q-difference case) - Maple Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Factorization and Solving Equations : QDifferenceEquations : QDifferenceEquations/Zeilberger

QDifferenceEquations[Zeilberger] - perform Zeilberger's algorithm (q-difference case)

Calling Sequence

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

Parameters

T

-

q-hypergeometric term in qn and qk

n

-

name

k

-

name

q

-

name

Qn

-

name; denote the q-shift operator with respect to qn

Description

• 

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

L=avqnQnv+...+a1qnQn+a0qn

  

and a q-hypergeometric term Gqn,qk of qn and qk such that

LoTqn,qk=Gqn,qk+1Gqn,qk

• 

Qn is the q-shift operator with respect to qn, defined by QnFqn,qk=Fqn+1,qk.

• 

By assigning values to the global variables _MINORDER and _MAXORDER, the algorithm is restricted to finding a Z-pair L,G for Tqn,qk 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 L,G representing the computed Z-pair L,G.

Examples

withQDifferenceEquations:

T:=qn+kQBinomialn,k,q

T:=qn+kQDifferenceEquations:-QBinomialn,k,q

(1)

Zpair:=ZeilbergerT,n,k,q,Qn:

Zpair1

Qn2+q2qQnqnq4+q3

(2)

Zpair2

qnq4qqn11+qkqkqn+kQDifferenceEquations:-QBinomialn,k,qqnq2+qkqqn+qk

(3)

T:=2qk2QPochhammerq,q,kQPochhammerq,q,nk

T:=2qk2QDifferenceEquations:-QPochhammerq,q,kQDifferenceEquations:-QPochhammerq,q,nk

(4)

Zpair:=ZeilbergerT,n,k,q,Qn:

Zpair1

qnq2+1Qn2+qn2q3+qnq2q1Qn+q

(5)

Zpair2

2qk2qn2q41+qkQDifferenceEquations:-QPochhammerq,q,kQDifferenceEquations:-QPochhammerq,q,nkqqn+qkqnq2+qk

(6)

See Also

SumTools[Hypergeometric][Zeilberger]

References

  

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


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam