# ## README < H Y P E R G > # # # ##### # # # # #### ##### ##### # # # # # # # # # # # # ####### # #### #### ##### # #### # # # # # # # # # # # # # ##### # # # # # # ##### # ## ## # # # # # # # ## # # ### ## ## This is the version 1.0 of HYPERG, a Maple package to manipulate generalized hypergeometric series. Description: HYPERG is a maple package for the manipulation of generalized hypergeometric series denoted by the usual symbol F(a_1,a_2,...; b_1,b_2,...; x)$. 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. Many features of this package are due to C. Krattenthaler and his mathematica package HYP. Many thanks to C. Krattenthaler, P. Paule, M. Petkovsek, A. Tefera and D. Zeilberger for their helpful comments. The package provides several tools (about sixty functions) for: o transforming sums into hypergeometric notation; o manipulating factorial expressions; o applying summation and transformation formulas; o applying contiguous relations; o computing formal limits of hypergeometric expressions; o finding polynomial, rational and hypergeometric solutions of recurrences; o using the Gosper and Zeilberger algorithms. # Copyright (c) 1998, 1999, 2000, Bruno Gauthier, Bruno.Gauthier@univ-mlv.fr # Institut Gaspard Monge # Universite Marne-la-Vallee # # Permission is granted to use, copy, and distribute this software for # non commercial use, provided that the above copyright notice appear # in all copies and that both this copyright notice and this permission # notice appear in supporting documentation. # # Permission to modify the software is granted, but not the right to # distribute the modified code. Please report bugs and changes to # Bruno.Gauthier@univ-mlv.fr # # This software is provided "as is" without expressed or implied warranty. For the moment, this program only works under Maple V Release 2 and Release 3. ## 1.0b HypContig improvement (C86, C118) Jun 2000 ## (thanks to Edgardo S. Cheb-Terrab) Jun 2000 ## 1.0a Oct 1999 ## 1.0 Jun 1999 ## 0.98a HypSolRec improvement (thanks to Akalu Tefera) Mar 1999 ## 0.98 PolySolRec and Gosper improvement Mar 1999 ## 0.97j T2111 Mar 1999 ## 0.97i HypConverg Feb 1999 ## 0.97h QRF modified and Gosper improvement Dec 1998 ## 0.97f MapApply, MapList (with depth) Nov 1998 ## 0.97d SumToHyp (with complex parameters) Oct 1998 ## 0.97b T1101 and fixed bugs Oct 1998 ## 0.97a HypDiff improvement Sep 1998 ## 0.97 PolySolQRec, RatioSolQRec, HypSolQRec, GenQRec Sep 1998 ## 0.96 HypType Jul 1998 ## 0.95 QBIN, IsQBIN, QBinEval Jul 1998 ## 0.94 HypSumList, HypTransfList Jun 1998 ## 0.90 transformation formulas T6501-T7694 Jun 1998 ## 0.88 transformation formulas T3204-T5403 Apr 1998 ## 0.87 summation formulas S7631-S7691 Apr 1998 ## 0.85 transformation formulas T2103-T2192 Apr 1998 ## 0.84 summation formulas S4306-S6532 Apr 1998 ## 0.83 RecOrder Apr 1998 ## 0.82 SimplifyRec, ShiftRec, SubsRec, CheckRec Mar 1998 ## 0.81 IsHomog, Homog Mar 1998 ## 0.80 HypDiff Feb 1998 ## 0.80 IsHyperg, HypergToRec Feb 1998 ## 0.80 contiguous formulas C104-C121 Feb 1998 ## 0.79 contiguous formulas C59-C103 Jan 1998 ## 0.78 very-well-poised basic hypergeometric series Jan 1998 ## 0.77 hypergeometric solutions of q-recurrences Nov 1997 ## 0.76 polynomial and rational solutions of q-recurrences Oct 1997 ## 0.75 basic hypergeometric series Oct 1997 ## 0.74 very-well-poised hypergeometric series Sep 1997 ## 0.73 MapList, MapApply Sep 1997 ## 0.72 contiguous formulas C53-C58 Sep 1997 ## 0.71 contiguous formulas C31-C52 Sep 1997 ## 0.65 contiguous formulas C01-C30 Aug 1997 ## 0.60 summation formulas S1001-S3291 Aug 1997 ## 0.50 rules for manipulating factorial expressions Jun 1997 ## 0.40 Gosper/Zeilberger algorithms Jun 1997 ## 0.30 hypergeometric solutions of recurrences May 1997 ## 0.20 polynomial and rational solutions of recurrences May 1997 ## 0.10 basics Apr 1997 The HYPERG distribution consists of the following files: README This message HYPERG The code file HYPERG.tst The test file HYPERG.ps.gz The user's reference manual (gzipped postscript-file) To install it, type: maple -s -q < HYPERG then update your ".mapleinit" file (change libname so that Maple V can find the package). (see details in the HYPERG user's reference manual.) To use it: $ maple |\^/| Maple V Release 3 (Univ-Marne La Vallee) ._|\| |/|_. Copyright (c) 1981-1994 by Waterloo Maple Software and the \ MAPLE / University of Waterloo. All rights reserved. Maple <____ ____> are registered trademarks of Waterloo Maple Software. | Type ? for help. > with(HYPERG); [AddParam, BaseSplit, CheckRec, Ext1, Ext2, FirstTerms, GenQRec, GenRec, Gosper, Homog, HypContig, HypContigList, HypConverg, HypDiff, HypEval, HypOrder, HypPermBoth, HypPermLow, HypPermUp, HypSimplify, HypSolQRec, HypSolRec, HypSum, HypSumList, HypSumPrint, HypToRec, HypToVHyp, HypTransf, HypTransfList, HypTransfPrint, HypType, HypergToRec, Inv, IsHYP, IsHomog, IsHyperg, IsQBIN, IsQHYP, IsQRF, IsRF, IsVHYP, IsWHYP, Lim, Linear1, Linear2, MapApply, MapList, Neg1, Neg2, PolySolQRec, PolySolRec, Prove, QBinEval, QHypEval, QHypOrder, QHypToWHyp, QHypType, QRfEval, RatioSolQRec, RatioSolRec, RecOrder, RfEval, ShiftRec, SimplifyRec, Split, SubsRec, SumToHyp, SumToRec, SummandToRec, Time, Trans, VHypToHyp, WHypToQHyp] See details in the user's reference manual. Please send problems and feedback to: Bruno Gauthier Bruno.Gauthier@univ-mlv.fr http://www-igm.univ-mlv.fr/~gauthier/ http://www-igm.univ-mlv.fr/~gauthier/HYPERG.html Universite Marne-la-Vallee Institut Gaspard Monge Cite Descartes, 5, Bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallee, Cedex 2, France