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QDifferenceEquations

  

IsQHypergeometricTerm

  

test if a given expression is a q-hypergeometric term

 

Calling Sequence

Parameters

Description

Examples

References

Calling Sequence

IsQHypergeometricTerm(H, n, q^n=N, R)

Parameters

H

-

function of q^n, algebraic expression

n

-

variable

q

-

name used as the parameter q, usually q

N

-

name

R

-

(optional) name; assigned the computed certificate

Description

• 

The IsQHypergeometricTerm(H,n,q^n=N,R) command returns true if H is a q-hypergeometric term of q^n. Otherwise, it returns false.

  

A function H is q-hypergeometric of q^n if Hqn+1Hqn=Rqn, a rational function of q^n. Rqn is the certificate of Hqn. If the fourth optional argument is included, it is assigned the certificate RN=Rqn.

• 

This implementation is mainly based on the implementation by H. Boeing and W. Koepf. See the References section.

Examples

withQDifferenceEquations:

Tqn1QPochhammera,q,nk=0n1q4qk+1qn2

T:=qn1QDifferenceEquations:-QPochhammera,q,nk=0n1q4qk+1qn2

(1)

IsQHypergeometricTermT,n,qn=N,'R'

true

(2)

R

Nq4+1Nq1Na1q2N1

(3)

TQBracketsn2,q

T:=QDifferenceEquations:-QBrackets12n,q

(4)

IsQHypergeometricTermT,n,qn=N

false

(5)

References

  

Boeing, H., and Koepf, W. "Algorithms for q-hypergeometric summation in computer algebra." Journal of Symbolic Computation. Vol. 11. (1999): 1-23.

See Also

QDifferenceEquations[QObjects]

QDifferenceEquations[QSimpComb]

 


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