Shaoshi Chen, Chinese Academy of Sciences, Beijing
"Creative
Telescoping
for
Algebraic
Functions"
The
problem
of
finding
linear
differential
equations
with
polynomial
coefficients
for
parametric
integrals
has
a
long
history.
It
at
least
dates
back
to
Picard
in
1902
who
proved
the
existence
of
such
equations
for
integrals
of
algebraic
functions
involving
parameters,
nowadays
so-called
Picard-Fuchs
equations.
This
has
been
generalized
to
higher-dimensional
cases
and
led
to
Gauss–Manin
connections.
The
key
in
computer
algebra
systems
for
obtaining
such
linear
differential
equations
is
the
method
of
creative
telescoping,
which
was
first
formulated
by
Zeilberger
in
the
1990s
as
an
algorithmic
tool
for
evaluating
definite
integrals
and
sums
with
parameters.
The
method
also
enables
us
to
prove
a
large
number
of
combinatorial
identities
in
an
automatic
way.
In
this
talk,
I
will
present
some
recent
work
on
creative
telescoping
for
algebraic
functions.
(Joint
work
with
Manuel
Kauers,
Christoph
Koutschan
and
Michael
F.
Singer)
MC
5403