XSummer: transcendental functions and symbolic summation in form

Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their generalizations appear as building blocks, originating for exa...

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Detalles Bibliográficos
Autores principales: Moch, S, Uwer, Peter
Lenguaje:eng
Publicado: 2005
Materias:
Mathematical Physics and Mathematics
Acceso en línea:https://dx.doi.org/10.1016/j.cpc.2005.12.014
http://cds.cern.ch/record/882710
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author Moch, S
Uwer, Peter
author_facet Moch, S
Uwer, Peter
author_sort Moch, S
collection CERN
description Harmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their generalizations appear as building blocks, originating for example from the expansion of generalized hypergeometric functions around integer values of the parameters. In this Letter we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form.
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institution Organización Europea para la Investigación Nuclear
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spelling cern-8827102019-09-30T06:29:59Zdoi:10.1016/j.cpc.2005.12.014http://cds.cern.ch/record/882710engMoch, SUwer, PeterXSummer: transcendental functions and symbolic summation in formMathematical Physics and MathematicsHarmonic sums and their generalizations are extremely useful in the evaluation of higher-order perturbative corrections in quantum field theory. Of particular interest have been the so-called nested sums,where the harmonic sums and their generalizations appear as building blocks, originating for example from the expansion of generalized hypergeometric functions around integer values of the parameters. In this Letter we discuss the implementation of several algorithms to solve these sums by algebraic means, using the computer algebra system Form.math-ph/0508008CERN-PH-TH-2005-124DESY-05-104DESY-2005-104SFB-CPP-2005-24oai:cds.cern.ch:8827102005-08-02
spellingShingle Mathematical Physics and Mathematics
Moch, S
Uwer, Peter
XSummer: transcendental functions and symbolic summation in form
title XSummer: transcendental functions and symbolic summation in form
title_full XSummer: transcendental functions and symbolic summation in form
title_fullStr XSummer: transcendental functions and symbolic summation in form
title_full_unstemmed XSummer: transcendental functions and symbolic summation in form
title_short XSummer: transcendental functions and symbolic summation in form
title_sort xsummer: transcendental functions and symbolic summation in form
topic Mathematical Physics and Mathematics
url https://dx.doi.org/10.1016/j.cpc.2005.12.014
http://cds.cern.ch/record/882710
work_keys_str_mv AT mochs xsummertranscendentalfunctionsandsymbolicsummationinform
AT uwerpeter xsummertranscendentalfunctionsandsymbolicsummationinform

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