Fetching the paper…
Reading the bibliography…
We determine closed and compact expressions for the epsilon-expansion of certain Gaussian hypergeometric functions expanded around half-integer values by explicitly solving for their recurrence relations.
J.A. Lappo-Danilevskij, “Mémoires sur la thorie des systémes des équations différentielles linéaires. Vol. IIIÓ, Travaux Inst. Physico-Math. Stekloff, 8, Acad. Sci. USSR, Moscow–Leningrad, 1936, 5–206
1936
Earlier work this paper cites.
K.G. Chetyrkin and F.V. Tkachov, “Integration by Parts: The Algorithm to Calculate beta Functions in 4 Loops,” Nucl. Phys. B 192
1981
Earlier work this paper cites.
E.E. Boos and A.I. Davydychev, “A method of evaluating massive Feynman integrals,” Theor. Math. Phys. 89
1991
Earlier work this paper cites.
A.B. Goncharov, “Multiple ζ \zeta -values, hyperlogarithms and mixed Tate motives,” preprint, 1993
1993
Earlier work this paper cites.
A.V. Kotikov, “Differential equations method: New technique for massive Feynman diagrams calculation,” Phys. Lett. B 254
1997
Earlier work this paper cites.
D.J. Broadhurst, “Massive three - loop Feynman diagrams reducible to SC* primitives of algebras of the sixth root of unity,” Eur. Phys. J. C 8
1999
Earlier work this paper cites.
E. Remiddi and J.A.M. Vermaseren, “Harmonic polylogarithms,” Int. J. Mod. Phys. A 15
2000
Earlier work this paper cites.
C. Anastasiou, E.W.N. Glover and C. Oleari, “Scalar one loop integrals using the negative dimension approach,” Nucl. Phys. B 572
2000
Earlier work this paper cites.
A.B. Goncharov, “Multiple polylogarithms and mixed Tate motives,” (2001), math.AG/0103059
2001
Earlier work this paper cites.
A.I. Davydychev and M.Y. Kalmykov, “New results for the epsilon expansion of certain one, two and three loop Feynman diagrams,” Nucl. Phys. B 605
2001
Cited alongside, same era.
S. Weinzierl, “Expansion around half integer values, binomial sums and inverse binomial sums,” J. Math. Phys. 45
2004
Cited alongside, same era.
F. Brown, “Single-valued hyperlogarithms and unipotent differential equations,” preprint, 2004
2004
Cited alongside, same era.
M.Y. Kalmykov, “Gauss hypergeometric function: Reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams,” JHEP 0604
2006
Cited alongside, same era.
M.Y. Kalmykov, B.F.L. Ward and S. Yost, “All order epsilon-expansion of Gauss hypergeometric functions with integer and half/integer values of parameters,” JHEP 0702
2007
Cited alongside, same era.
2009
Later among the works it cites.
V.A. Smirnov, “Evaluating Feynman Integrals,” Springer Berlin Heidelberg, November 2010
2010
Later among the works it cites.
2012
Later among the works it cites.
J.M. Henn, “Multiloop integrals in dimensional regularization made simple,” Phys. Rev. Lett. 110
2013
Later among the works it cites.
R.H. Boels, “On the field theory expansion of superstring five point amplitudes,” Nucl. Phys. B 876
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
2007
Cited alongside, same era.
L.J. Slater, “Generalized hypergeometric functions,” Cambridge University Press (2008)
2008
Cited alongside, same era.
A.V. Smirnov, “Algorithm FIRE – Feynman Integral REduction,” JHEP 0810
2008
Cited alongside, same era.
D. Oprisa and S. Stieberger, “Six gluon open superstring disk amplitude, multiple hypergeometric series and Euler-Zagier sums,” hep-th/0509042
Cited in the paper.
Cited in the paper.
Work in progress
Cited in the paper.
2013
Later among the works it cites.
2014
Later among the works it cites.