DescriptionHYPERG is a Maple package (about sixty functions) devoted to symbolic computation on hypergeometric series. It also provides tools for automatic proofs of identities, but they are just tools: every step in a series of manipulations has to be controlled by the user.
The goal of this package is to make the algorithms in this area better known, and to help you enter the wonderful world of hypergeometric series.
This package is available for Maple V Release 2, 3 for any Ms-Dos, Windows [3.x, 95] and Unix-Linux system.
Download INSTRUCTION README;
HYPERG, the Maple code file;
HYPERG.tst, the test file;
HYPERG.ps.gz, the full gziped postscript file of the user's reference manual.
INSTALL.ps.gz, get the first 13 pages of the user's reference manual as a gziped postscript file. It includes a brief introduction of HYPERG, and a few tips to install the package on your machine.
List of functionsAddParam - add a parameter to a [basic] hypergeometric series in standard notation
BaseSplit - Rules to handle any factorial expression (Gamma function, and Rising Factorial)
CheckRec - tests if a term satisfies a recurrence relation
Ext1 & Ext2 - Rules to handle any factorial expression (Gamma function, and Rising Factorial)
FirstTerms - extracts first terms of a summation
GenQRec - generate a q-recurrence
GenRec - generate a recurrence
Gosper - Gosper's algorithm for summation
Homog - Homogenizes a recurrence equation
HypContig - Contiguous formula in form of rules
HypContigPrint - Print a contiguous formula in form of an equation
HypConverg - test if is a convergent hypergeometric series
HypDiff - Differentiation of a hypergeometric series
HypEval - Rule that transforms a HYP[] into a Sum()
HypOrder - Order parameters of a hypergeometric series
HypPerm[Up/Low/Both] - Rules for permuting parameters in [basic] hypergeometric series
HypSimplify - Apply simplification rules to [basic] hypergeometric series
HypSolQRec - linear q-recurrence equation solver - hypergeometric solutions
HypSolRec - linear recurrence equation solver - hypergeometric solutions
HypSum - Summation formula in form of rules
HypSumList - gives a list of applicable summation formulas
HypSumPrint - Print a summation formula in form of an equation
HypToRec - Zeilberger's algorithm
HypToVHyp - convert hypergeometric series into hypergeometric series in very-well-poised order
HypTransf - Transformation formula in form of rules
HypTransList - gives a list of applicable transformation formulas
HypTransfPrint - Print a transformation formula in form of an equation
HypType - Print the type of a hypergeometric series
HypergToRec - return a linear first-order homogeneous recurrence satisfied by a hypergeometric term
Inv - Rules to handle any factorial expression (Gamma function, and Rising Factorial)
IsHYP - test if is a hypergeometric series
IsHomog - tests if a recurrence equation is homogeneous
IsHyperg - test if is a hypergeometric term
IsQBIN - test if is a q-binomial coefficient
IsQHYP - test if is a basic hypergeometric series
IsQRF - test if is a q-rising factorial
IsRF - test if is a rising factorial
IsVHYP - test if is a hypergeometric series in very-well-poised order
IsWHYP - test if is a basic hypergeometric series in very-well-poised order
Lim - compute formal limit of hypergeometric expressions
Linear1 & Linear2 - Rules to handle any factorial expression (Gamma function, and Rising Factorial)
MapList & MapApply - Functions for controlled application of rules and functions
Neg1 & Neg2 - Rules to handle any factorial expression (Gamma function, and Rising Factorial)
PolySolQRec - linear q-recurrence equation solver - polynomial solutions
PolySolRec - linear recurrence equation solver - polynomial solutions
Prove - Zeilberger's algorith (automatic proof)
QBinEval - Rule that evals q-binomial coefficients
QHypEval - Rule that transforms a QHYP[] into a Sum()
QHypOrder - Order parameters of a basic hypergeometric series
QHypToWHyp - convert basic hypergeometric series into basic hypergeometric series in very-well-poised order
QHypType - Print the type of a basic hypergeometric series
QRfEval - Rule that evals q-rising factorials
RatioSolQRec - linear q-recurrence equation solver - rational solutions
RatioSolRec - linear recurrence equation solver - rational solutions
RecOrder - computes the order of a recurrence equation
RfEval - Rule that evals rising factorials
ShiftRec - shifts a recurrence equation
SimplifyRec - simplifies a recurrence equation
Split - Rules to handle any factorial expression (Gamma function, and Rising Factorial)
SubsRec - substitutes (in a recurrence) the sequence by a term
SumToHyp - convert summations into hypergeometric series
SumToRec - Zeilberger's algorithm
SummandToRec - Zeilberger's algorithm
Time - gives time information
Trans - Rules to handle any factorial expression (Gamma function, and Rising Factorial)
VHypToHyp - convert hypergeometric series in very-well-poised order into hypergeometric series in standard notation
WHypToQHyp - convert basic hypergeometric series in very-well-poised order into basic hypergeometric series in standard notation