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We consider finite iterated generalized harmonic sums weighted by the binomial $\binom{2k}{k}$ in numerators and denominators.
H. Mellin, Über den Zusammenhang zwischen den linearen Differential- und Differenzen- gleichungen
1902
Earlier work this paper cites.
N. Nielsen, Handbuch der Theorie der Gammafunktion
1906
Earlier work this paper cites.
E. Landau, Über die Grundlagen der Theorie der Fakultätenreihen
1906
Earlier work this paper cites.
J. Hadamard, Lectures on Cauchy’s problem in linear partial differential equations
1923
Earlier work this paper cites.
Ø. Ore, The Theory of Non-Commutative Polynomials
1933
Earlier work this paper cites.
L. Schwartz, Théorie des distributions
1951
Earlier work this paper cites.
R. Ree, Lie elements and an algebra associated with shuffles , Ann. Math. 68
1958
Earlier work this paper cites.
S.L. Glashow, Partial Symmetries of Weak Interactions
1961
Earlier work this paper cites.
S. Weinberg, A Model of Leptons
1967
Earlier work this paper cites.
R.H. Risch, The problem of integration in finite terms , Trans. Amer. Math. Soc. 139
1969
Earlier work this paper cites.
G. ’t Hooft, Renormalization of Massless Yang-Mills Fields
1971
Earlier work this paper cites.
G. ’t Hooft, Renormalizable Lagrangians for Massive Yang-Mills Fields
1971
Earlier work this paper cites.
G. ’t Hooft and M.J.G. Veltman, Regularization and Renormalization of Gauge Fields
1972
Earlier work this paper cites.
D.J. Gross and F. Wilczek, Ultraviolet Behavior of Nonabelian Gauge Theories
1973
Earlier work this paper cites.
H.D. Politzer, Reliable Perturbative Results for Strong Interactions?
1973
Earlier work this paper cites.
H. Fritzsch, M. Gell-Mann and H. Leutwyler, Advantages of the Color Octet Gluon Picture
1973
Earlier work this paper cites.
G. ’t Hooft and M.J.G. Veltman, Diagrammar
1974
Earlier work this paper cites.
G. ’t Hooft and M.J.G. Veltman, Scalar One Loop Integrals
1979
Earlier work this paper cites.
B.M. Trager, Integration of simple radical extensions , Proceedings of EUROSAM’79
1979
Earlier work this paper cites.
L. Lewin, Polylogarithms and Associated Functions
1981
Earlier work this paper cites.
Summation in finite terms
M. Karr, · 1981
Earlier work this paper cites.
G.E.T. Almkvist and D. Zeilberger, The method of differentiating under the integral sign
1990
Earlier work this paper cites.
M. Petkovšek, Hypergeometric solutions of linear recurrences with polynomial coefficients
1992
Earlier work this paper cites.
Free Lie algebras
C. Reutenauer, · 1993
Earlier work this paper cites.
S.S. Schweber, QED and the men who made it. Dyson, Feynman, Schwinger, and Tomonaga
1994
Earlier work this paper cites.
M.J.G. Veltman, Diagrammatica: The Path to Feynman Diagrams
1994
Earlier work this paper cites.
S.A. Abramov and M. Petkovšek, D’Alembertian solutions of linear differential and difference equations
1994
Earlier work this paper cites.
S. Laporta and E. Remiddi, The analytical value of the electron ( g − 2 ) (g-2) at order α 3 \alpha^{3} in QED
1996
Earlier work this paper cites.
M. Buza, Y. Matiounine, J. Smith, R. Migneron and W.L. van Neerven, Heavy quark coefficient functions at asymptotic values Q 2 ≫ m 2 Q^{2}\gg m^{2}
1996
Earlier work this paper cites.
T. van Ritbergen, J.A.M. Vermaseren and S.A. Larin, The four loop β \beta -function in quantum chromodynamics
1997
Earlier work this paper cites.
M. Buza, Y. Matiounine, J. Smith and W.L. van Neerven, O ( α s 2 ) O(\alpha_{s}^{2}) corrections to polarized heavy flavor production at Q 2 ≫ m 2 Q^{2}\gg m^{2}
1997
Earlier work this paper cites.
M. Buza and W.L. van Neerven, O ( α s 2 ) O(\alpha_{s}^{2}) contributions to charm production in charged current deep inelastic lepton-hadron scattering
1997
Earlier work this paper cites.
M. Buza, Y. Matiounine, J. Smith and W.L. van Neerven, Charm electroproduction viewed in the variable flavor number scheme versus fixed order perturbation theory
1998
Earlier work this paper cites.
O. M. Ogreid and P. Osland, J. Comput. Appl. Math. 98
1998
Cited alongside, same era.
J. Blümlein and S. Kurth, Harmonic sums and Mellin transforms up to two loop order
1999
Cited alongside, same era.
J. Fleischer, A.V. Kotikov and O.L. Veretin, Analytic two loop results for selfenergy type and vertex type diagrams with one nonzero mass
1999
Cited alongside, same era.
P.A. Hendriks and M.F. Singer, Solving difference equations in finite terms
1999
Cited alongside, same era.
E. Remiddi and J.A.M. Vermaseren, Harmonic polylogarithms
2000
Cited alongside, same era.
Quasi-shuffle products
M. Hoffman, · 2000
Cited alongside, same era.
R. Osburn and C. Schneider, Gaussian hypergeometric series and extensions of supercongruences
2009
Later among the works it cites.
2009
Later among the works it cites.
J. Blümlein, D.J. Broadhurst and J.A.M. Vermaseren, The Multiple Zeta Value Data Mine
2010
Later among the works it cites.
J. Blümlein, Structural Relations of Harmonic Sums and Mellin Transforms at Weight w = 6 · 2010
Later among the works it cites.
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M. Y. Kalmykov and O. Veretin, Single scale diagrams and multiple binomial sums
2000
Cited alongside, same era.
J. Blümlein, Analytic continuation of Mellin transforms up to two loop order
2000
Cited alongside, same era.
F. Chyzak, An extension of Zeilberger’s fast algorithm to general holonomic functions , Discrete Mathematics 217
2000
Cited alongside, same era.
M. Bronstein, On solutions of linear ordinary difference equations in their coefficient field
2000
Cited alongside, same era.
J.M. Borwein, D.M. Bradley, D.J. Broadhurst and P. Lisonek, Special values of multiple polylogarithms,
2001
Cited alongside, same era.
J.M. Borwein and D.J. Broadhurst and J. Kamnitzer, Central binomial sums, multiple Clausen values, and zeta values
2001
Cited alongside, same era.
2010
Later among the works it cites.
C.B. Koutschan, HolonomicFunctions (User’s Guide)
2010
Later among the works it cites.
C.B. Koutschan, A Fast Approach to Creative Telescoping , Mathematics in Computer Science 4
2010
Later among the works it cites.
C. Schneider, Structural Theorems for Symbolic Summation
2010
Later among the works it cites.
C. Schneider, A Symbolic Summation Approach to Find Optimal Nested Sum Representations · 2010
Later among the works it cites.
C. Schneider, Parameterized Telescoping Proves Algebraic Independence of Sums
2010
Later among the works it cites.
2011
Later among the works it cites.
2011
Later among the works it cites.
2011
Later among the works it cites.
J. Blümlein, A. Hasselhuhn and C. Schneider, Evaluation of Multi-Sums for Large Scale Problems
2011
Later among the works it cites.
M. Kauers and P. Paule, The Concrete Tetrahedron
2011
Later among the works it cites.
2012
Later among the works it cites.
2012
Later among the works it cites.
C.G. Raab, Definite Integration in Differential Fields , PhD Thesis, Johannes Kepler Universität Linz, Austria, 2012
2012
Later among the works it cites.
W. Decker, G.-M. Greuel, G. Pfister and H. Schönemann, Singular 3-1-6 — A computer algebra system for polynomial computations
2012
Later among the works it cites.
Sh. Chen, M. Kauers, M.F. Singer, Telescopers for Rational and Algebraic Functions via Residues , Proceedings of ISSAC 2012 (2012) 130–137
2012
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
2013
Later among the works it cites.
C. Schneider, Simplifying Multiple Sums in Difference Fields
2013
Later among the works it cites.
A. Bostan, Sh. Chen, F. Chyzak, Z. Li, G. Xin, Hermite Reduction and Creative Telescoping for Hyperexponential Functions , Proceedings of ISSAC 2013, pp. 77-84, 2013
2013
Later among the works it cites.
C. Schneider, Fast Algorithms for Refined Parameterized Telescoping in Difference Fields
2013
Later among the works it cites.
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