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Numerical evaluation of two-dimensional harmonic polylogarithms
The two-dimensional harmonic polylogarithms $\G(\vec{a}(z);y)$, a generalization of the harmonic polylogarithms, themselves a generalization of Nielsen's polylogarithms, appear in analytic calculations of multi-loop radiative corrections in quantum field theory. We present an algorithm for the...
| Autores principales: | , |
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| Lenguaje: | eng |
| Publicado: |
2001
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| Materias: | |
| Acceso en línea: | https://dx.doi.org/10.1016/S0010-4655(02)00139-X http://cds.cern.ch/record/527721 |
| _version_ | 1780897941467168768 |
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| author | Gehrmann, T. Remiddi, E. |
| author_facet | Gehrmann, T. Remiddi, E. |
| author_sort | Gehrmann, T. |
| collection | CERN |
| description | The two-dimensional harmonic polylogarithms $\G(\vec{a}(z);y)$, a generalization of the harmonic polylogarithms, themselves a generalization of Nielsen's polylogarithms, appear in analytic calculations of multi-loop radiative corrections in quantum field theory. We present an algorithm for the numerical evaluation of two-dimensional harmonic polylogarithms, with the two arguments $y,z$ varying in the triangle $0\le y \le 1$, $ 0\le z \le 1$, $\ 0\le (y+z) \le 1$. This algorithm is implemented into a {\tt FORTRAN} subroutine {\tt tdhpl} to compute two-dimensional harmonic polylogarithms up to weight 4. |
| id | cern-527721 |
| institution | Organización Europea para la Investigación Nuclear |
| language | eng |
| publishDate | 2001 |
| record_format | invenio |
| spelling | cern-5277212023-10-04T08:16:08Zdoi:10.1016/S0010-4655(02)00139-Xhttp://cds.cern.ch/record/527721engGehrmann, T.Remiddi, E.Numerical evaluation of two-dimensional harmonic polylogarithmsParticle Physics - PhenomenologyThe two-dimensional harmonic polylogarithms $\G(\vec{a}(z);y)$, a generalization of the harmonic polylogarithms, themselves a generalization of Nielsen's polylogarithms, appear in analytic calculations of multi-loop radiative corrections in quantum field theory. We present an algorithm for the numerical evaluation of two-dimensional harmonic polylogarithms, with the two arguments $y,z$ varying in the triangle $0\le y \le 1$, $ 0\le z \le 1$, $\ 0\le (y+z) \le 1$. This algorithm is implemented into a {\tt FORTRAN} subroutine {\tt tdhpl} to compute two-dimensional harmonic polylogarithms up to weight 4.The two-dimensional harmonic polylogarithms $\G(\vec{a}(z):y)$, a generalization of the harmonic polylogarithms, themselves a generalization of Nielsen's polylogarithms, appear in analytic calculations of multi-loop radiative corrections in quantum field theory. We present an algorithm for the numerical evaluation of two-dimensional harmonic polylogarithms, with the two arguments $y,z$ varying in the triangle $0\le y \le 1$, $ 0\le z \le 1$, $\ 0\le (y+z) \le 1$. This algorithm is implemented into a {\tt FORTRAN} subroutine {\tt tdhpl} to compute two-dimensional harmonic polylogarithms up to weight 4.hep-ph/0111255CERN-TH-2001-326CERN-TH-2001-326oai:cds.cern.ch:5277212001-11-21 |
| spellingShingle | Particle Physics - Phenomenology Gehrmann, T. Remiddi, E. Numerical evaluation of two-dimensional harmonic polylogarithms |
| title | Numerical evaluation of two-dimensional harmonic polylogarithms |
| title_full | Numerical evaluation of two-dimensional harmonic polylogarithms |
| title_fullStr | Numerical evaluation of two-dimensional harmonic polylogarithms |
| title_full_unstemmed | Numerical evaluation of two-dimensional harmonic polylogarithms |
| title_short | Numerical evaluation of two-dimensional harmonic polylogarithms |
| title_sort | numerical evaluation of two-dimensional harmonic polylogarithms |
| topic | Particle Physics - Phenomenology |
| url | https://dx.doi.org/10.1016/S0010-4655(02)00139-X http://cds.cern.ch/record/527721 |
| work_keys_str_mv | AT gehrmannt numericalevaluationoftwodimensionalharmonicpolylogarithms AT remiddie numericalevaluationoftwodimensionalharmonicpolylogarithms |