diff --git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index cdc7266..66d3083 100644
--- a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ -6248,6 +6248,376 @@ Proc ISSAC 97 pp172-175 (1997)
\end{chunk}
+\section{Symbolic Summation} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+\index{Karr, Michael}
+\begin{chunk}{axiom.bib}
+@Article{Karr85,
+ author = "Karr, Michael",
+ title = "Theory of Summation in Finite Terms",
+ year = "1985",
+ journal = "Journal of Symbolic Computation",
+ volume = "1",
+ number = "3",
+ month = "September",
+ pages = "303-315",
+ paper = "Karr85.pdf",
+ abstract = "
+ This paper discusses some of the mathematical aspects of an algorithm
+ for finding formulas for finite sums. The results presented here
+ concern a property of difference fields which show that the algorithm
+ does not divide by zero, and an analogue to Liouville's theorem on
+ elementary integrals."
+}
+
+\end{chunk}
+
+\index{Karr, Michael}
+\begin{chunk}{axiom.bib}
+@article{Karr81,
+ author = "Karr, Michael",
+ title = "Summation in Finite Terms",
+ journal = "Journal Association for Computing Machinery",
+ year = "1981",
+ volume = "28",
+ number = "2",
+ month = "April",
+ issn = "0004-5411",
+ pages = "305--350",
+ url = "http://doi.acm.org/10.1145/322248.322255",
+ publisher = "ACM",
+ paper = "Karr81",
+ abstract = "
+ Results which allow either the computation of symbolic solutions to
+ first-order linear difference equations or the determination that
+ solutions of a certain form do not exist are presented. Starting with
+ a field of constants, larger fields may be constructed by the formal
+ adjunction of symbols which behave like solutions to first-order
+ linear equations (with a few restrictions). It is in these extension
+ fields that the difference equations may be posed and in which the
+ solutions are requested. The principal application of these results is
+ in finding formulas for a broad class of finite sums or in showing the
+ nonexistence of such formula."
+}
+
+\end{chunk}
+
+\index{Zima, Eugene V.}
+\begin{chunk}{axiom.bib}
+@article{Zima13,
+ author = "Zima, Eugene V.",
+ title = "Accelerating Indefinite Summation: Simple Classes of Summands",
+ journal = "Mathematics in Computer Science",
+ year = "2013",
+ month = "December",
+ volume = "7",
+ number = "4",
+ pages = "455--472",
+ paper = "Zima13.pdf",
+ abstract = "
+ We present the history of indefinite summation starting with classics
+ (Newton, Montmort, Taylor, Stirling, Euler, Boole, Jordan) followed by
+ modern classics (Abramov, Gosper, Karr) to the current implementation
+ in computer algebra system Maple. Along with historical presentation
+ we describe several ``acceleration techniques'' of algorithms for
+ indefinite summation which offer not only theoretical but also
+ practical improvements in running time. Implementations of these
+ algorithms in Maple are compared to standard Maple summation tools"
+}
+
+\end{chunk}
+
+\index{Er\"ocal, Bur\c{c}in}
+\begin{chunk}{axiom.bib}
+@article{Eroc10,
+ author = {Er\"ocal, Bur\c{c}in},
+ title = "Summation in Finite Terms Using Sage",
+ journal = "ACM Commun. Comput. Algebra",
+ volume = "44",
+ number = "3/4",
+ month = "January",
+ year = "2011",
+ issn = "1932-2240",
+ pages = "190--193",
+ url = "http://doi.acm.org/10.1145/1940475.1940517",
+ publisher = "ACM",
+ paper = "Eroc10.pdf",
+ abstract = "
+ The summation analogue of the Risch integration algorithm developed by
+ Karr uses towers of difference fields to model nested indefinite sums
+ and products, as the Risch algorithm uses towers of differential
+ fields to model the so called {\sl elementary functions}. The
+ algorithmic machinery developed by Karr, and later generalized and
+ extended, allows one to find solutions of first order difference
+ equations over such towers of difference fields, in turn simplifying
+ expressions involving sums and products.
+
+ We present an implementation of this machinery in the open source
+ computer algebra system Sage. Due to the nature of open source
+ software, this allows direct experimentation with the algorithms and
+ structures involved while taking advantage of the state of the art
+ primitives provided by Sage. Even though these methods are used behind
+ the scenes in the summation package Sigma and they were previously
+ implemented, this is the first open source implementation."
+}
+
+\end{chunk}
+
+\index{Er\"ocal, Bur\c{c}in}
+\begin{chunk}{axiom.bib}
+@phdthesis{Eroc11,
+ author = {Er\"ocal, Bur\c{c}in},
+ title = "Algebraic Extensions for Symbolic Summation",
+ school = "RISC Research Institute for Symbolic Computation",
+ year = "2011",
+ url =
+ "http://www.risc.jku.at/publications/download/risc_4320/erocal_thesis.pdf",
+ paper = "Eroc11.pdf",
+ abstract = "
+
+ The main result of this thesis is an effective method to extend Karr's
+ symbolic summation framework to algebraic extensions. These arise, for
+ example, when working with expressions involving $(-1)^n$. An
+ implementation of this method, including a modernised version of
+ Karr's algorithm is presented.
+
+ Karr's algorithm is the summation analogue of the Risch algorithm for
+ indefinite integration. In the summation case, towers of specialized
+ difference fields called $\prod\sum$-fields are used to model nested
+ sums and products. This is similar to the way elementary functions
+ involving nested logarithms and exponentials are represented in
+ differential fields in the integration case.
+
+ In contrast to the integration framework, only transcendental
+ extensions are allowed in Karr's construction. Algebraic extensions of
+ $\prod\sum$-fields can even be rings with zero divisors. Karr's
+ methods rely heavily on the ability to solve first-order linear
+ difference equations and they are no longer applicable over these
+ rings.
+
+ Based on Bronstein's formulation of a method used by Singer for the
+ solution of differential equations over algebraic extensions, we
+ transform a first-order linear equation over an algebraic extension to
+ a system of first-order equations over a purely transcendental
+ extension field. However, this domain is not necessarily a
+ $\prod\sum$-field. Using a structure theorem by Singer and van der
+ Put, we reduce this system to a single first-order equation over a
+ $\prod\sum$-field, which can be solved by Karr's algorithm. We also
+ describe how to construct towers of difference ring extensions on an
+ algebraic extension, where the same reduction methods can be used.
+
+ A common bottleneck for symbolic summation algorithms is the
+ computation of nullspaces of matrices over rational function
+ fields. We present a fast algorithm for matrices over $\mathbb{Q}(x)$
+ which uses fast arithmetic at the hardware level with calls to BLAS
+ subroutines after modular reduction. This part is joint work with Arne
+ Storjohann."
+}
+
+\end{chunk}
+
+\index{Schneider, Carsten}
+\begin{chunk}{axiom.bib}
+@article{Schn05,
+ author = "Schneider, Carsten",
+ title = "A new Sigma approach to multi-summation",
+ year = "2005",
+ journal = "Advances in Applied Mathematics",
+ volume = "34",
+ number = "4",
+ pages = "740--767",
+ paper = "Schn05.pdf",
+ abstract = "
+ We present a general algorithmic framework that allows not only to
+ deal with summation problems over summands being rational expressions
+ in indefinite nested syms and products (Karr, 1981), but also over
+ $\delta$-finite and holonomic summand expressions that are given by a
+ linear recurrence. This approach implies new computer algebra tools
+ implemented in Sigma to solve multi-summation problems efficiently.
+ For instacne, the extended Sigma package has been applied successively
+ to provide a computer-assisted proof of Stembridge's TSPP Theorem."
+\end{chunk}
+
+\index{Kauers, Manuel}
+\begin{chunk}{axiom.bib}
+@article{Kaue07,
+ author = "Kauers, Manuel",
+ title = "Summation algorithms for Stirling number identities",
+ year = "2007",
+ journal = "Journal of Symbolic Computation",
+ volume = "42",
+ number = "10",
+ month = "October",
+ pages = "948--970",
+ paper = "Kaue07.pdf",
+ abstract = "
+ We consider a class of sequences defined by triangular recurrence
+ equations. This class contains Stirling numbers and Eulerian numbers
+ of both kinds, and hypergeometric multiples of those. We give a
+ sufficient criterion for sums over such sequences to obey a recurrence
+ equation, and present algorithms for computing such recurrence
+ equations efficiently. Our algorithms can be used for verifying many
+ known summation identities on Stirling numbers instantly, and also for
+ discovering new identities."
+}
+
+\end{chunk}
+
+\index{Schneider, Carsten}
+\index{Kauers, Manuel}
+\begin{chunk}{axiom.bib}
+@article{Kaue08,
+ author = "Kauers, Manuel and Schneider, Carsten",
+ title = "Indefinite summation with unspecified summands",
+ year = "2006",
+ journal = "Discrete Mathematics",
+ volume = "306",
+ number = "17",
+ pages = "2073--2083",
+ paper = "Kaue80.pdf",
+ abstract = "
+ We provide a new algorithm for indefinite nested summation which is
+ applicable to summands involving unspecified sequences $x(n)$. More
+ than that, we show how to extend Karr's algorithm to a general
+ summation framework by which additional types of summand expressions
+ can be handled. Our treatment of unspecified sequences can be seen as
+ a first illustrative application of this approach."
+}
+
+\end{chunk}
+
+\index{Schneider, Carsten}
+\begin{chunk}{axiom.bib}
+@article{Schn08,
+ author = "Schneider, Carsten",
+ title = "A refined difference field theory for symbolic summation",
+ year = "2008",
+ journal = "Journal of Symbolic Computation",
+ volume = "43",
+ number = "9",
+ pages = "611--644",
+ paper = "Schn08.pdf",
+ abstract = "
+ In this article we present a refined summation theory based on Karr's
+ difference field approach. The resulting algorithms find sum
+ representations with optimal nested depth. For instance, the
+ algorithms have been applied successively to evaluate Feynman
+ integrals from Perturbative Quantum Field Theory"
+}
+
+\end{chunk}
+
+\index{Schneider, Carsten}
+\begin{chunk}{axiom.bib}
+@article{Schn09,
+ author = "Schneider, Carsten",
+ title = "Structural theorems for symbolic summation",
+ journal = "Proc. AAECC-2010",
+ year = "2010",
+ volume = "21",
+ pages = "1--32",
+ paper = "Schn09.pdf",
+ abstract = "
+ Starting with Karr's structural theorem for summation - the discrete
+ version of Liouville's structural theorem for integration - we work
+ out crucial properties of the underlying difference fields. This leads
+ to new and constructive structural theorems for symbolic summation.
+ E.g., these results can be applied for harmonic sums which arise
+ frequently in particle physics."
+}
+
+\end{chunk}
+
+\index{Schneider, Carsten}
+\begin{chunk}{axiom.bib}
+@phdthesis{Schn01,
+ author = "Schneider, Carsten",
+ title = "Symbolic Summation in Difference Fields",
+ school = "RISC Research Institute for Symbolic Computation",
+ year = "2001",
+ url =
+ "http://www.risc.jku.at/publications/download/risc_3017/SymbSumTHESIS.pdf",
+ paper = "Schn01.pdf",
+ abstract = "
+
+ There are implementations of the celebrated Gosper algorithm (1978) on
+ almost any computer algebra platform. Within my PhD thesis work I
+ implemented Karr's Summation Algorithm (1981) based on difference
+ field theory in the Mathematica system. Karr's algorithm is, in a
+ sense, the summation counterpart of Risch's algorithm for indefinite
+ integration. Besides Karr's algorithm which allows us to find closed
+ forms for a big clas of multisums, we developed new extensions to
+ handle also definite summation problems. More precisely we are able to
+ apply creative telescoping in a very general difference field setting
+ and are capable of solving linear recurrences in its context.
+
+ Besides this we find significant new insights in symbolic summation by
+ rephrasing the summation problems in the general difference field
+ setting. In particular, we designed algorithms for finding appropriate
+ difference field extensions to solve problems in symbolic summation.
+ For instance we deal with the problem to find all nested sum
+ extensions which provide us with additional solutions for a given
+ linear recurrence of any order. Furthermore we find appropriate sum
+ extensions, if they exist, to simplify nested sums to simpler nested
+ sum expressions. Moreover we are able to interpret creative
+ telescoping as a special case of sum extensions in an indefinite
+ summation problem. In particular we are able to determine sum
+ extensions, in case of existence, to reduce the order of a recurrence
+ for a definite summation problem."
+
+}
+
+\end{chunk}
+
+\index{Schneider, Carsten}
+\begin{chunk}{axiom.bib}
+@InProceedings{Schn07,
+ author = "Schneider, Carsten",
+ title = "Symbolic Summation Assists Combinatorics",
+ year = "2007",
+ booktitle = "S\'eminaire Lotharingien de Combinatoire",
+ volume = "56",
+ article = "B56b",
+ url = "",
+ paper = "Schn07.pdf",
+ abstract = "
+ We present symbolic summation tools in the context of difference
+ fields that help scientists in practical problem solving. Throughout
+ this article we present multi-sum examples which are related to
+ combinatorial problems."
+}
+
+\end{chunk}
+
+\index{Schneider, Carsten}
+\begin{chunk}{axiom.bib}
+@InProceedings{Schn00,
+ author = "Schneider, Carsten",
+ title = "An implementation of Karr's summation algorithm in Mathematica",
+ year = "2000",
+ booktitle = "S\'eminaire Lotharingien de Combinatoire",
+ volume = "S43b",
+ pages = "1-10",
+ url = "",
+ paper = "Schn00.pdf",
+ abstract = "
+ Implementations of the celebrated Gosper algorithm (1978) for
+ indefinite summation are available on almost any computer algebra
+ platform. We report here about an implementation of an algorithm by
+ Karr, the most general indefinite summation algorithm known. Karr's
+ algorithm is, in a sense, the summation counterpart of Risch's
+ algorithm for indefinite integration. This is the first implementation
+ of this algorithm in a major computer algebra system. Our version
+ contains new extensions to handle also definite summation problems. In
+ addition we provide a feature to find automatically appropriate
+ difference field extensions in which a closed form for the summation
+ problem exists. These new aspects are illustrated by a variety of
+ examples."
+
+}
+
+\end{chunk}
+
\section{To Be Classified} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Kaltofen, Erich}
diff --git a/changelog b/changelog
index f498757..3af7c95 100644
--- a/changelog
+++ b/changelog
@@ -1,3 +1,5 @@
+20141008 tpd src/axiom-website/patches.html 20141008.03.tpd.patch
+20141008 tpd books/bookvolbib add a section on Symbolic Summation
20141008 jtw src/axiom-website/patches.html 20141008.02.jtw.patch
20141008 jtw books/bookvolbib add Whee12 biblio reference
20141008 jtw books/bookvol10.1 add chapter on differential forms
diff --git a/patch b/patch
index cd6fcae..60bc62c 100644
--- a/patch
+++ b/patch
@@ -1,3 +1,3 @@
-books/bookvol10.1 add chapter on differential forms
+books/bookvolbib add a section on Symbolic Summation
-James Wheeler contributed documentation on differential forms
+Collect references to papers on symbolic summation using Karr's method
diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html
index 0a16fe8..c79b4ca 100644
--- a/src/axiom-website/patches.html
+++ b/src/axiom-website/patches.html
@@ -4676,6 +4676,8 @@ books/bookvol10.3 DERHAM: fix signature of 'degree'

books/bookvol10.3 DERHAM: add code for differential forms

20141008.02.jtw.patch
books/bookvol10.1 add chapter on differential forms

+20141008.03.tpd.patch
+books/bookvolbib add a section on Symbolic Summation