Maple Professional
Maple Academic
Maple Student Edition
Maple Personal Edition
Maple Player
Maple Player for iPad
MapleSim Professional
MapleSim Academic
Maple T.A. - Testing & Assessment
Maple T.A. MAA Placement Test Suite
Möbius - Online Courseware
Machine Design / Industrial Automation
Aerospace
Vehicle Engineering
Robotics
Power Industries
System Simulation and Analysis
Model development for HIL
Plant Modeling for Control Design
Robotics/Motion Control/Mechatronics
Other Application Areas
Mathematics Education
Engineering Education
High Schools & Two-Year Colleges
Testing & Assessment
Students
Financial Modeling
Operations Research
High Performance Computing
Physics
Live Webinars
Recorded Webinars
Upcoming Events
MaplePrimes
Maplesoft Blog
Maplesoft Membership
Maple Ambassador Program
MapleCloud
Technical Whitepapers
E-Mail Newsletters
Maple Books
Math Matters
Application Center
MapleSim Model Gallery
User Case Studies
Exploring Engineering Fundamentals
Teaching Concepts with Maple
Maplesoft Welcome Center
Teacher Resource Center
Student Help Center
SumTools[Hypergeometric][IsZApplicable] - test the applicability of Zeilberger's algorithm to hypergeometric terms
Calling Sequence
IsZApplicable(F, n, k, En, 'Zpair')
Parameters
F
-
hypergeometric term in n and k
n
name
k
En
(optional) name; denote the shift operator with respect to n
'Zpair'
(optional) name; assigned computed Z-pair
Description
Let F be a hypergeometric term in n and k. The IsZApplicable(F, n, k, En, 'Zpair') command determines the applicability of Zeilberger's algorithm to F. It returns true if Zeilberger's algorithm is applicable to F. Otherwise, it returns false.
If Zeilberger's algorithm is applicable to the function F and the fourth and the fifth optional arguments are specified, the fifth argument 'Zpair' is assigned the computed Z-pair for F.
If the input F is not a rational function of n and k, IsZApplicable returns FAIL. In this case, if the optional arguments En and 'Zpair' are specified, Zeilberger(F, n, k, En) is called. If it succeeds in finding a Z-pair for F, the computed Z-pair is assigned to 'Zpair'.
Examples
In the following example, F is not a proper hypergeometric term. However, Zeilberger's algorithm is applicable to F:
In the following example, F is not a proper hypergeometric term, and Zeilberger's algorithm is not applicable to F either:
The input is a hypergeometric term of n and k.
See Also
SumTools[Hypergeometric], SumTools[Hypergeometric][IsProperHypergeometricTerm], SumTools[Hypergeometric][MinimalZpair], SumTools[Hypergeometric][Verify], SumTools[Hypergeometric][Zeilberger], SumTools[Hypergeometric][ZpairDirect]
References
Abramov, S.A. "Applicability of Zeilberger's Algorithm to Hypergeometric Terms." Proceedings ISSAC'2002, pp. 1-7. ACM Press, 2002.
Abramov, S.A., and Le, H.Q. "Applicability of Zeilberger's Algorithm to Rational Functions." Proceedings FPSAC'2000, pp. 91-102. Springer-Verlag LNCS, 2000.
Download Help Document
