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In this work we present the computer algebra package HarmonicSums and its theoretical background for the manipulation of harmonic sums and some related quantities as for example Euler-Zagier sums and harmonic polylogarithms.
Treue Darstellung Liescher Ringe
E. Witt · 1937
Earlier work this paper cites.
Mémoirs sur la Théorie des Systèms Différentielles Linéaires
J.A. Lappo-Danielevsky · 1953
Earlier work this paper cites.
Die Unterringe der freien Lieschen Ringe
E. Witt · 1956
Earlier work this paper cites.
Free differential calculus IV. the quotient groups of the lower central series
K.T. Chen, R.H. Fox, and R.C. Lyndon · 1958
Earlier work this paper cites.
Free Lie Algebras
C. Reutenauer · 1969
Earlier work this paper cites.
A natural ring basis for the shuffle algebra and an application to group schemes
D. Radford · 1979
Earlier work this paper cites.
Summation in finite terms
M. Karr · 1981
Earlier work this paper cites.
Computer algebra symbolic and algebraic computation
B. Buchberger, G. E. Collins, R. Loos, and R. Albrecht, editors · 1983
Earlier work this paper cites.
Combinatorics on words
M. Lothaire · 1983
Earlier work this paper cites.
Ramanujan’s Notebooks
B. Berndt · 1985
Earlier work this paper cites.
Multiple harmonic series
M. Hoffman · 1992
Earlier work this paper cites.
Values of zeta functions and their applications
D. Zagier · 1994
Earlier work this paper cites.
Some q-series identities related to divisor functions
K. Dilcher · 1995
Earlier work this paper cites.
A note on alternating sums
P. Kirschenhofer · 1996
Earlier work this paper cites.
Special Functions. An Introduction to the Classical Functions of Mathematical Physics
N. Temme · 1996
Cited alongside, same era.
The algebra of multiple harmonic series
M. Hoffman · 1997
Cited alongside, same era.
Harmonic sums and mellin transforms up to two-loop order
J. Blümlein and S. Kurth · 1999
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Harmonic sums, Mellin transforms and integrals
J.A.M. Vermaseren · 1999
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Analytic continuation of mellin transforms up to two-loop order
J. Blümlein · 2000
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Quasi-shuffle products
M. Hoffman · 2000
Cited alongside, same era.
Structure and asymptotic expansion of multiple harmonic sums
Analytic continuation of the harmonic sums for the 3- loop anomalous dimensions
J. Blümlein and S. Moch · 2005
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The third-order QCD corrections to deep-inelastic scattering by photon exchange
J.A.M. Vermaseren, A. Vogt, and S. Moch · 2005
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Hpl, a Mathematica implementation of the harmonic polylogarithms
D. Maître · 2006
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Symbolic summation assists combinatorics
C. Schneider · 2007
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Structural relations between nested harmonic sums
J. Blümlein · 2008
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A refined difference field theory for symbolic summation
C. Schneider · 2008
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Hoang Ngoc Minh and J. van der Hoeven M. Petitot · 2000
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Harmonic polylogarithms
E. Remiddi and J.A.M. Vermaseren · 2000
Cited alongside, same era.
Asymptotics and Mallin-Barnes Integrals
R. B. Paris and D. Kaminski · 2001
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Lyndon words and shuffle algebras for generating the coloured multiple zeta values relations tables
M. Bigotte, G. Jacob, and M. Petitot N.E. Oussous · 2002
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Nested sums, expansion of transcendental functions, and multiscale multiloop integrals
S. Moch, P. Uwer, and S. Weinzierl · 2002
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Lehrbuch der Analysis, Teil 1
H. Heuser · 2003
Cited alongside, same era.
In preparation
J. Ablinger, J. Blümlein, and C. Schneider · 2009
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Structural relations of harmonic sums and mellin transforms at weight w=6
J. Blümlein · 2009
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Structural relations of harmonic sums and mellin transforms up to weight w=5
J. Blümlein · 2009
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Determining the closed forms of the o ( a s 3 ) o(a_{s}^{3}) anomalous dimensions and wilson coefficients from mellin moments by means of computer algebra
J. Blümlein, M. Kauers, S. Klein, and C. Schneider · 2009
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From moments to functions in quantum chromodynamics
J. Blümlein, M. Kauers, S. Klein, and C. Schneider · 2009
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Parameterized telescoping proves algebraic independence of sums
C. Schneider · 2009
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A symbolic summation approach to find optimal nested sum representation
C. Schneider · 2009
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