Nestedsums

Nestedsums library. Symbolic Expansion of Transcendental Functions. Higher transcendental function occur frequently in the calculation of Feynman integrals in quantum field theory. Their expansion in a small parameter is a non-trivial task. We report on a computer program which allows the systematic expansion of certain classes of functions. The algorithms are based on the Hopf algebra of nested sums. The program is written in C++ and uses the GiNaC library.


References in zbMATH (referenced in 21 articles , 1 standard article )

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  1. Adams, Luise; Bogner, Christian; Weinzierl, Stefan: The iterated structure of the all-order result for the two-loop sunrise integral (2016)
  2. Bogner, Christian; Brown, Francis: Feynman integrals and iterated integrals on moduli spaces of curves of genus zero (2015)
  3. Panzer, Erik: Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals (2015)
  4. Greynat, David; Sesma, Javier; Vulvert, Grégory: Derivatives of the Pochhammer and reciprocal Pochhammer symbols and their use in epsilon-expansions of Appell and Kampé de Fériet functions (2014)
  5. Ablinger, Jakob; Blümlein, Johannes: Harmonic sums, polylogarithms, special numbers, and their generalizations (2013)
  6. Ablinger, Jakob; Blümlein, Johannes; Schneider, Carsten: Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms (2013)
  7. Boels, Rutger H.: On the field theory expansion of superstring five point amplitudes (2013)
  8. Bierenbaum, Isabella; Czakon, Michał; Mitov, Alexander: The singular behavior of one-loop massive QCD amplitudes with one external soft gluon (2012)
  9. Grozin, A.G.: Massless two-loop self-energy diagram: historical review (2012)
  10. Bogner, Christian; Weinzierl, Stefan: Feynman graphs in perturbative quantum field theory (2011)
  11. Bork, L.V.; Kazakov, D.I.; Vartanov, G.S.: On form factors in $\mathcalN = 4$ SYM (2011)
  12. Bytev, Vladimir V.; Kalmykov, Mikhail Yu.; Kniehl, Bernd A.: Differential reduction of generalized hypergeometric functions from Feynman diagrams: one-variable case (2010)
  13. Huber, Tobias; Ma{^i}tre, Daniel: Hypexp 2, expanding hypergeometric functions about half-integer parameters (2008)
  14. Huber, T.; Ma{^i}tre, D.: Hypexp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters (2006)
  15. Ma{^i}tre, D.: HPL, a Mathematica implementation of the harmonic polylogarithms (2006)
  16. Blümlein, Johannes: Algebraic relations between harmonic sums and associated quantities. (2004)
  17. Weinzierl, Stefan: Gtybalt-a free computer algebra system (2004)
  18. Weinzierl, Stefan: Expansion around half-integer values, binomial sums, and inverse binomial sums. (2004)
  19. Moch, Sven; Uwer, Peter; Weinzierl, Stefan: Nested sums, expansion of transcendental functions, and multiscale multiloop integrals. (2002)
  20. Weinzierl, Stefan: Symbolic expansion of transcendental functions (2002) ioport

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