354 research outputs found
Numerical Implementation of Harmonic Polylogarithms to Weight w = 8
We present the FORTRAN-code HPOLY.f for the numerical calculation of harmonic
polylogarithms up to w = 8 at an absolute accuracy of
or better. Using algebraic and argument relations the numerical representation
can be limited to the range . We provide replacement
files to map all harmonic polylogarithms to a basis and the usual range of
arguments to the above interval analytically. We also
briefly comment on a numerical implementation of real valued cyclotomic
harmonic polylogarithms.Comment: 19 pages LATEX, 3 Figures, ancillary dat
Computing the Inverse Mellin Transform of Holonomic Sequences using Kovacic's Algorithm
We describe how the extension of a solver for linear differential equations
by Kovacic's algorithm helps to improve a method to compute the inverse Mellin
transform of holonomic sequences. The method is implemented in the computer
algebra package HarmonicSums.Comment: 8 pages. arXiv admin note: text overlap with arXiv:1606.0284
Special functions, transcendentals and their numerics
Cyclotomic polylogarithms are reviewed and new results concerning the special
constants that occur are presented. This also allows some comments on previous
literature results using PSLQ
Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams
Nested sums containing binomial coefficients occur in the computation of
massive operator matrix elements. Their associated iterated integrals lead to
alphabets including radicals, for which we determined a suitable basis. We
discuss algorithms for converting between sum and integral representations,
mainly relying on the Mellin transform. To aid the conversion we worked out
dedicated rewrite rules, based on which also some general patterns emerging in
the process can be obtained.Comment: 13 pages LATEX, one style file, Proceedings of Loops and Legs in
Quantum Field Theory -- LL2014,27 April 2014 -- 02 May 2014 Weimar, German
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