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An expression in terms of (cyclotomic) harmonic sums can be simplified by the quasi-shuffle algebra in terms of the so-called basis sums.
Difference Algebra
R. M. Cohn · 1965
Earlier work this paper cites.
On the summation of rational functions
S. A. Abramov · 1971
Earlier work this paper cites.
Summation in finite terms
M. Karr · 1981
Earlier work this paper cites.
Theory of summation in finite terms
M. Karr · 1985
Earlier work this paper cites.
Rational solutions of linear differential and difference equations with polynomial coefficients
S. A. Abramov · 1989
Earlier work this paper cites.
Multiple harmonic series
M. Hoffman · 1992
Earlier work this paper cites.
D’Alembertian solutions of linear differential and difference equations
S. A. Abramov and M. Petkovšek · 1994
Earlier work this paper cites.
A = B A=B
M. Petkovšek, H. S. Wilf, and D. Zeilberger · 1996
Earlier work this paper cites.
The algebra of multiple harmonic series
M. Hoffman · 1997
Earlier work this paper cites.
A canonical form guide to symbolic summation
I. Nemes and P. Paule · 1997
Earlier work this paper cites.
Galois theory of difference equations
M. van der Put and M.F. Singer · 1997
Earlier work this paper cites.
Harmonic sums and Mellin transforms up to two-loop order
J. Blümlein and S. Kurth · 1999
Earlier work this paper cites.
Analytic two loop results for selfenergy type and vertex type diagrams with one nonzero mass
J. Fleischer, A. V. Kotikov, and O. L. Veretin · 1999
Earlier work this paper cites.
Solving difference equations in finite terms
P. A. Hendriks and M. F. Singer · 1999
Earlier work this paper cites.
Harmonic sums, Mellin transforms and integrals
J.A.M. Vermaseren · 1999
Earlier work this paper cites.
Analytic continuation of mellin transforms up to two-loop order
J. Blümlein · 2000
Earlier work this paper cites.
On solutions of linear ordinary difference equations in their coefficient field
M. Bronstein · 2000
Earlier work this paper cites.
Quasi-shuffle products
M. Hoffman · 2000
Earlier work this paper cites.
Harmonic polylogarithms
E. Remiddi and J.A.M. Vermaseren · 2000
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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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Computer proofs of a new family of harmonic number identities
P. Paule and C. Schneider · 2003
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Algebraic relations between harmonic sums and associated quantities
J. Blümlein · 2004
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Massive Feynman diagrams and inverse binomial sums
A. I. Davydychev and M. Y. Kalmykov · 2004
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A collection of denominator bounds to solve parameterized linear difference equations in Π Σ {\Pi}{\Sigma} -extensions
C. Schneider · 2004
Cited alongside, same era.
Structural theorems for symbolic summation
C. Schneider · 2010
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A symbolic summation approach to find optimal nested sum representations
C. Schneider · 2010
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Harmonic sums and polylogarithms generated by cyclotomic polynomials
J. Ablinger, J. Blümlein, and C. Schneider · 2011
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Unfair permutations
H. Prodinger, C. Schneider, and S. Wagner · 2011
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Computer algebra algorithms for special functions in particle physics
J. Ablinger · 2012
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Analytic and algorithmic aspects of generalized harmonic sums and polylogarithms
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Structure and asymptotic expansion of multiple harmonic sums
C. Costermans, J.Y.Enjalbert, Hoang Ngoc Minh, and M. Petitot · 2005
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C. Schneider · 2007
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Solving linear recurrence equations with polynomial coefficients
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The package HarmonicSums: Computer algebra and analytic aspects of nested sums
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Iterated Binomial Sums and their Associated Iterated Integrals
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C. Schneider · 2014
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Fast algorithms for refined parameterized telescoping in difference fields
C. Schneider · 2015
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A difference ring theory for symbolic summation
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Summation Theory II: Characterizations of R Π Σ R\Pi\Sigma -extensions and algorithmic aspects
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