Hi,

> is there someone on this list that knows a good book reference about
> the Karr summation algorithm ?

There are about 3 references which are more than a research paper:

1.) Symbolic Summation in Difference Fields (Karr + modern extensions) [Carsten 
Schneider]
2.) Algebraic Extensions for Symbolic Summation (Has good intro/summary 
chapter) [Burcin Erocal]
3.) Summation in Finite Terms, Presentation and Implementation of M.Karr's 
Algorithm [J. Grätner]

This is I think all I know about. There is nothing like Bronstein's book for 
summation.

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