HYP and HYPQ
The Mathematica package HYP
HYP is a package, written in Mathematica, for the manipulation and
identification of binomial and hypergeometric series and identities.
This package provides tools for
- (A) manipulating factorial expressions
- (B) transforming binomial sums into hypergeometric
notation
- (C) summing hypergeometric series
- (D) transforming hypergeometric series
- (E) applying contiguous relations
- (F) doing formal limits of hypergeometric
expressions
- (G) transforming hypergeometric expressions
into TeX-code
- (H) Using the Gosper and Zeilberger algorithms
(For item (H) you need Peter Paule
and Markus
Schorn's Mathematica
implementation of the Gosper and Zeilberger algorithms which are
available directly via
the WEB or via e-mail request to peter.paule at risc dot uni-linz dot ac dot at.
You will also want to get
Marko
Petkovsek's (Marko.Petkovsek at fmf dot uni-lj dot si)
Mathematica program Hyper which
finds all "hypergeometric term" solutions of a linear recurrence with
polynomial coefficients.)
The package comes with complete documentation, a tutorial, and an installation guide.
They should work with any version of
Mathematica, except that Gosper's and Zeilberger's
algorithms require Version 2.0 at least.
Retrieve the files directly on WWW:
- hyp.m, the basic input
- contig.m, the input for contiguous relations
- summatio.m, the input for summations in form of rules
- summatio.mgl, the input for summations in form of equations
- transfor.m, the input for transformations in form
of rules
- transfor.mgl, the input for transformations in form
of equations
- transfor.mli, the input for lists of transformations
- output, a file that makes a nicer screen output
- read.me, the installation guide
- hypm.tex, the AmS-TeX file for the documentation (453 K)
- hypm.dvi, the dvi-file for the documentation (590 K)
- hypm.ps.gz, the gzipped postscript-file for the documentation
(206 K)
- hypm.pdf, the PDF file for the documentation (552 K)
- hyp_hypq.tex, the AmS-TeX file for a
tutorial
- hyp_hypq.dvi, the dvi-file for a tutorial
- hyp_hypq.ps.gz, the gzipped
postsript-file for a tutorial (45 K)
- hyp_hypq.pdf, the PDF file for a
tutorial
- "HYP and HYPQ",
a short article that appeared in J. Symbol. Comput. 20 (1995),
737-744.
Read the file read.chg
for the differences between the current version and older versions.
If you want to be informed about updates of these packages, have comments,
suggestions, problems,...
send an e-mail to:
kratt at ap dot univie dot ac dot at
There is also a ``q-analogue", the package
HYPQ which allows you to manipulate and
identify basic hypergeometric series.
Back to Christian Krattenthaler's
home page.
The Mathematica package HYPQ
HYPQ is a package, written in Mathematica, for the manipulation and
identification of q-binomial and basic hypergeometric series and identities.
This package provides tools for
- (A) manipulating q-factorial expressions
- (B) transforming q-binomial sums into
basic hypergeometric notation
- (C) summing basic hypergeometric series
- (D) transforming basic hypergeometric series
- (E) applying contiguous relations
- (F) doing formal limits of basic hypergeometric
expressions
- (G) transforming basic hypergeometric expressions
into TeX-code
- (H) Using the q-Gosper and q-Zeilberger algorithms (to come shortly)
(For item (H) you need Peter Paule
and Axel
Riese's Mathematica
implementation of the q-Gosper and q-Zeilberger algorithms which are
(soon) available directly via
the WEB or via e-mail request to peter.paule at risc dot uni-linz dot ac dot at.
You will also want to get
Marko
Petkovsek's (Marko.Petkovsek at fmf dot uni-lj dot si)
Mathematica program q-Hyper which
finds all "q-hypergeometric term" solutions of a q-difference
equation with rational coefficients.)
The package comes with complete documentation, a tutorial, and an installation guide.
They should work with any version of
Mathematica, except that the q-Gosper and q-Zeilberger
algorithms require Version 2.0 at least.
Retrieve the files directly on WWW:
- hyp.q, the basic input
- contig.q, the input for contiguous relations
- summatio.q, the input for summations in form of rules
- summatio.qgl, the input for summations in form of equations
- transfor.q, the input for transformations in form
of rules
- transfor.qgl, the input for transformations in form
of equations
- transfor.qli, the input for lists of transformations
- output, a file that makes a nicer screen output
- read.me, the installation guide
- hypq.tex, the AmS-TeX file for the documentation (594 K)
- hypq.dvi, the dvi-file for the documentation (781 K)
- hypq.ps.gz, the gzipped postscript-file for the documentation
(280 K)
- hypq.pdf, the PDF file for the documentation (666 K)
- hyp_hypq.tex, the AmS-TeX file for a tutorial
- hyp_hypq.dvi, the dvi-file for a tutorial
- hyp_hypq.ps.gz, the gzipped postscript-file
for a tutorial (45 K)
- "HYP and HYPQ",
a short article that appeared in J. Symbol. Comput. 20 (1995),
737-744.
Read the file read.chg
for the differences between the current version and older versions.
If you want to be informed about updates of these packages, have comments,
suggestions, problems,... send an e-mail to:
kratt at ap dot univie dot ac dot at
There is also the package
HYP which allows you to manipulate and
identify ordinary hypergeometric series.
Back to Christian Krattenthaler's
home page.