42 research outputs found
Series Evaluation of a Quartic Integral
We present a new single sum series evaluation of Moll's quartic integral and
present two new generalizationsComment: 4 page
Computer algebra tools for Feynman integrals and related multi-sums
In perturbative calculations, e.g., in the setting of Quantum Chromodynamics
(QCD) one aims at the evaluation of Feynman integrals. Here one is often faced
with the problem to simplify multiple nested integrals or sums to expressions
in terms of indefinite nested integrals or sums. Furthermore, one seeks for
solutions of coupled systems of linear differential equations, that can be
represented in terms of indefinite nested sums (or integrals). In this article
we elaborate the main tools and the corresponding packages, that we have
developed and intensively used within the last 10 years in the course of our
QCD-calculations
The 1958 Pekeris-Accad-WEIZAC Ground-Breaking Collaboration that Computed Ground States of Two-Electron Atoms (and its 2010 Redux)
In order to appreciate how well off we mathematicians and scientists are
today, with extremely fast hardware and lots and lots of memory, as well as
with powerful software, both for numeric and symbolic computation, it may be a
good idea to go back to the early days of electronic computers and compare how
things went then. We have chosen, as a case study, a problem that was
considered a huge challenge at the time. Namely, we looked at C.L. Pekeris's
seminal 1958 work on the ground state energies of two-electron atoms. We went
through all the computations ab initio with today's software and hardware, with
a special emphasis on the symbolic computations which in 1958 had to be made by
hand, and which nowadays can be automated and generalized.Comment: 8 pages, 2 photos, final version as it appeared in the journa
The computational challenge of enumerating high-dimensional rook walks
We provide guessed recurrence equations for the counting sequences of rook
paths on d-dimensional chess boards starting at (0..0) and ending at (n..n),
where d=2,3,...,12. Our recurrences suggest refined asymptotic formulas of
these sequences. Rigorous proofs of the guessed recurrences as well as the
suggested asymptotic forms are posed as challenges to the reader