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From the reviews: "This is a great book, which will hopefully
become a classic in the subject of differential Galois theory. ...]
the specialist, as well as the novice, have long been missing an
introductory book covering also specific and advanced research
topics. This gap is filled by the volume under review, and more
than satisfactorily." Mathematical Reviews
This book lays the algebraic foundations of a Galois theory of
linear difference equations and shows its relationship to the
analytic problem of finding meromorphic functions asymptotic to
formal solutions of difference equations. Classically, this latter
question was attacked by Birkhoff and Tritzinsky and the present
work corrects and greatly generalizes their contributions. In
addition results are presented concerning the inverse problem in
Galois theory, effective computation of Galois groups, algebraic
properties of sequences, phenomena in positive characteristics, and
q-difference equations. The book is aimed at advanced graduate
researchers and researchers.
This volume gives an up-to-date review of the subject Integration
in Finite Terms. The book collects four significant
texts together with an extensive bibliography and
commentaries discussing these works and their impact. These
texts, either out of print or never published before,
are fundamental to the subject of the book. Applications in
combinatorics and physics have aroused a renewed interest in this
well-developed area devoted to finding solutions of
differential equations and, in particular, antiderivatives,
expressible in terms of classes of elementary and special
functions.
This volume gives an up-to-date review of the subject Integration
in Finite Terms. The book collects four significant texts together
with an extensive bibliography and commentaries discussing these
works and their impact. These texts, either out of print or never
published before, are fundamental to the subject of the book.
Applications in combinatorics and physics have aroused a renewed
interest in this well-developed area devoted to finding solutions
of differential equations and, in particular, antiderivatives,
expressible in terms of classes of elementary and special
functions.
This book is a collection of three introductory tutorials coming
out of three courses given at the CIMPA Research School ``Galois
Theory of Difference Equations'' in Santa Marta, Columbia, July
23-August 1, 2012. The aim of these tutorials is to introduce the
reader to three Galois theories of linear difference equations and
their interrelations. Each of the three articles addresses a
different galoisian aspect of linear difference equations. The
authors motivate and give elementary examples of the basic ideas
and techniques, providing the reader with an entry to current
research. In addition each article contains an extensive
bibliography that includes recent papers; the authors have provided
pointers to these articles allowing the interested reader to
explore further.
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