From: Roger Germundsson <germund@isl.stanford.edu>
Newsgroups: sci.math.symbolic
Subject: Re: Q:on formal summation
Date: Sat, 02 Nov 1996 08:40:51 -0800

Jacques Oberdoerffer wrote:
> 
> What are Moenk's method and Zeilberger-Koepf's algorithm ?
> I know Gosper's algorithm , but where to get references for the others?
> All my thanks for help .
>           Jacques Oberdoerffer
>           oberdoer@worldnet.net

These are the references you asked for ... and some more. --Roger

@InProceedings{Moenck:77a,
 Author         = { R. Moenck },
 Title          = { On Computing Closed Forms for Summation },
 BookTitle      = { Proceedings of Macsyma Conference },
 Year           = { 1977 },
 Pages          = { 225--236 }
}

Zeilberger has written quite a number of articles either using this
algorithm or 
extending it in various ways. Another nice treatment of the algorithm
can be 
found in Graham, Knuth, Patashnik "Concrete Mathematics" second edition. 

@Article{Zeilberger:91a,
 Author         = { D. Zeilberger },
 Title          = { The method of creative telescoping },
 Journal        = { Journal of Symbolic Computation },
 Year           = { 1991 },
 Volume         = { 11 },
 Number         = { 3 },
 Pages          = { 195 -- 204 },
 Month          = { March },
 Abstract       = { An algorithm for definite hypergeometric summation
is
  given. It is based, in a non-obvious way, on the Gosper algorithm for
  definite hypergeometric summation, and its theoretical justification
relies
  on the Bernstein theory of holonomic systems. },
 Language       = { English }
}

You can access this stuff from Konrad Zuse Zentrum server in Berlin. 

@TechReport{Koepf:94c,
  Author        = {W. Koepf},
  Title         = {{REDUCE} Package fo the Indefinite and Definite
Summation}, 
  Institution   = {Konrad-Zuse-Zentrum fur Infromationstechnik},
  Year          = {1994},
  Number        = {TR 94-9},
  Address       = {Berlin, Germany},
  Month         = {November},
  Annotation    = {An implementation of Gospers and Zeilbergers
algorithms}
}

If you are that interested in summataion you might as well get one of
the 
most up to date takes on state of the art ...
This has now been published in JSC, but I don't have the exact
coordinates. 
It is this year and as far as I know only January through March issues
have 
been published. 

@Article{PauleS:95a,
  Author        = {P. Paule and V. Strehl},
  Title         = {Symbolic Summation -- Some Recent Developments},
  Journal       = {Journal of Symbolic Computation},
  Year          = {1995},
  Note          = {To appear},
  Annotation    = {Also available from RISC homepage. The best article
        I've seen on summation so far.}
}

The deepest theory of summation ... albeit not fully algorithmic yet is 
probably by Karr. 

@Article{Karr:81a,
 Author         = { M. Karr },
 Title          = { Summation in Finite Terms },
 Journal        = { Journal of ACM },
 Year           = { 1981 },
 Volume         = { 28 },
 Number         = { 2 },
 Pages          = { 305--350 }
}