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We present fully analytic results for all master integrals for the three-loop banana graph with four equal and non-zero masses.
1902
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1907
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M. Czakon, https://mbtools.hepforge.org/ ,
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D. J. Broadhurst, The Master Two Loop Diagram With Masses
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S. Bauberger, F. A. Berends, M. Bohm, and M. Buza, Analytical and numerical methods for massive two loop selfenergy diagrams
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O. V. Tarasov, Connection between Feynman integrals having different values of the space-time dimension
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C. Anastasiou, E. W. N. Glover, and C. Oleari, The two-loop scalar and tensor pentabox graph with light-like legs
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C. Anastasiou, T. Gehrmann, C. Oleari, E. Remiddi, and J. B. Tausk, The Tensor reduction and master integrals of the two loop massless crossed box with lightlike legs
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C. Anastasiou, J. B. Tausk, and M. E. Tejeda-Yeomans, The On-shell massless planar double box diagram with an irreducible numerator
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T. Gehrmann and E. Remiddi, Differential equations for two loop four point functions
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T. Gehrmann and E. Remiddi, Two loop master integrals for γ ∗ → 3 \gamma^{*}\to 3 jets: The Planar topologies
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V. A. Smirnov, Applied asymptotic expansions in momenta and masses · 2002
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P. Mastrolia and E. Remiddi, The Analytic value of a three loop sunrise graph in a particular kinematical configuration
2003
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S. Laporta and E. Remiddi, Analytic treatment of the two loop equal mass sunrise graph
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B. A. Kniehl, A. V. Kotikov, A. Onishchenko, and O. Veretin, Two-loop sunset diagrams with three massive lines
2006
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math/0502576
Y. I. Manin, Iterated integrals of modular forms and noncommutative modular symbols · 2006
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R. S. Maier, On Rationally Parametrized Modular Equations
2006
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M. Czakon, Automatized analytic continuation of Mellin-Barnes integrals
2006
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2008
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D. Broadhurst, Feynman integrals, L-series and Kloosterman moments
2016
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2017
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G. Passarino, Elliptic Polylogarithms and Basic Hypergeometric Functions
2017
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2017
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2009
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M. Czakon and A. Mitov, Inclusive Heavy Flavor Hadroproduction in NLO QCD: The Exact Analytic Result
2010
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2010
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F. Brown and O. Schnetz, A K3 in ϕ 4 \phi^{4}
2012
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2012
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S. Caron-Huot and K. J. Larsen, Uniqueness of two-loop master contours
2012
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R. Huang and Y. Zhang, On Genera of Curves from High-loop Generalized Unitarity Cuts
2013
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2017
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S. Laporta, High-precision calculation of the 4-loop contribution to the electron g-2 in QED
2017
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E. Remiddi and L. Tancredi, An Elliptic Generalization of Multiple Polylogarithms
2017
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2017
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H. Frellesvig and C. G. Papadopoulos, Cuts of Feynman Integrals in Baikov representation
2017
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J. Bosma, M. Sogaard, and Y. Zhang, Maximal Cuts in Arbitrary Dimension
2017
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2018
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2018
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2018
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2018
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2018
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2018
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2018
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2018
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L. Adams and S. Weinzierl, Feynman integrals and iterated integrals of modular forms
2018
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2018
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2018
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J. Broedel, C. Duhr, F. Dulat, B. Penante, and L. Tancredi, From modular forms to differential equations for Feynman integrals · 2018
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2019
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2019
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