1997. - 209 pages.
Contents.
Quick Start.
Background.
Proof Machines.
Evolution of the province of human thought.
Canonical and normal forms.
Polynomial identities.
Proofs by example?
Trigonometric identities.
Fibonacci identities.
Symmetric function identities.
Elliptic function identities.
Tightening the Target.
Identities.
Human and computer proofs; an example.
A Mathematica session.
A Maple session.
Where we are and what happens next.
The Hypergeometric Database.
Hypergeometric series.
How to identify a series as hypergeometric.
Software that identifies hypergeometric series.
Some entries in the hypergeometric database.
Using the database.
Is there really a hypergeometric database?
The Five Basic Algorithms.
Sister Celine's Method.
Sister Mary Celine Fasenmyer.
Sister Celine's general algorithm.
The Fundamental Theorem.
Multivariate and q-generalizations.
Gosper's Algorithm.
Introduction.
Hypergeometrics to rationals to polynomials.
The full algorithm: Step.
The full algorithm: Step.
Similarity among hypergeometric terms.
Zeilberger's Algorithm.
Existence of the telescoped recurrence.
How the algorithmworks.
Use of the programs.
The WZ Phenomenon.
WZ proofs of the hypergeometric database.
Spinos from the WZ method.
Discovering new hypergeometric identities.
Software for the WZ method.
Algorithm Hyper.
The ring of sequences.
Polynomial solutions.
Hypergeometric solutions.
A Mathematica session.
Finding all hypergeometric solutions.
Finding all closed form solutions.
Some famous sequences that do not have closed form.
Inhomogeneous recurrences.
Factorization of operators.
An Operator Algebra Viewpoint.
Early history.
Linear difference operators.
Elimination in two variables.
Modified elimination problem.
Discrete holonomic functions.
Elimination in the ring of operators.
Contents.
Quick Start.
Background.
Proof Machines.
Evolution of the province of human thought.
Canonical and normal forms.
Polynomial identities.
Proofs by example?
Trigonometric identities.
Fibonacci identities.
Symmetric function identities.
Elliptic function identities.
Tightening the Target.
Identities.
Human and computer proofs; an example.
A Mathematica session.
A Maple session.
Where we are and what happens next.
The Hypergeometric Database.
Hypergeometric series.
How to identify a series as hypergeometric.
Software that identifies hypergeometric series.
Some entries in the hypergeometric database.
Using the database.
Is there really a hypergeometric database?
The Five Basic Algorithms.
Sister Celine's Method.
Sister Mary Celine Fasenmyer.
Sister Celine's general algorithm.
The Fundamental Theorem.
Multivariate and q-generalizations.
Gosper's Algorithm.
Introduction.
Hypergeometrics to rationals to polynomials.
The full algorithm: Step.
The full algorithm: Step.
Similarity among hypergeometric terms.
Zeilberger's Algorithm.
Existence of the telescoped recurrence.
How the algorithmworks.
Use of the programs.
The WZ Phenomenon.
WZ proofs of the hypergeometric database.
Spinos from the WZ method.
Discovering new hypergeometric identities.
Software for the WZ method.
Algorithm Hyper.
The ring of sequences.
Polynomial solutions.
Hypergeometric solutions.
A Mathematica session.
Finding all hypergeometric solutions.
Finding all closed form solutions.
Some famous sequences that do not have closed form.
Inhomogeneous recurrences.
Factorization of operators.
An Operator Algebra Viewpoint.
Early history.
Linear difference operators.
Elimination in two variables.
Modified elimination problem.
Discrete holonomic functions.
Elimination in the ring of operators.