Christoph Koutschan
The 1958 Pekeris-Accad-WEIZAC Ground-Breaking Collaboration that computed Ground States of Two-Electron Atoms (and its 2010 Redux).
Wed, 06/02/2010 - 15:01 — SomNambulAuthors: Doron Zeilberger, Christoph Koutschan
Subjects: Symbolic Computation
AbstractIn order to appreciate how good we as mathematicians and scientists have it
today, with extremely fast hardware and lots and lots of memory, as well as
with readily available high-level software, both for numeric and symbolic
computation, it may be a good idea to go back to the early days of electronic
computers and carefully examine, as a case study, a problem that was considered
a huge challenge back then, and compare notes. We chose C.L. Pekeris' 1958
seminal work on the ground state energies of two-electron atoms.A Fast Approach to Creative Telescoping.
Wed, 04/21/2010 - 15:02 — SomNambulAuthors: Christoph Koutschan
Subjects: Symbolic Computation
AbstractIn this note we reinvestigate the task of computing creative telescoping
relations in differential-difference operator algebras. Our approach is based
on an ansatz that explicitly includes the denominators of the delta parts. We
contribute several ideas of how to make an implementation of this approach
reasonably fast and provide such an implementation. A selection of examples
shows that it can be superior to existing methods by a large factor.A Proof of George Andrews' and David Robbins' $q$-TSPP Conjecture.
Wed, 02/24/2010 - 16:01 — SomNambulAuthors: Doron Zeilberger, Manuel Kauers, Christoph Koutschan
Subjects: Combinatorics
AbstractThe conjecture that the orbit-counting generating function for totally
symmetric plane partitions can be written as an explicit product-formula, has
been stated independently by George Andrews and David Robbins around 1983. We
present a proof of this long-standing conjecture.
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