scholarly journals Iterated binomial sums and their associated iterated integrals

2014 ◽  
Vol 55 (11) ◽  
pp. 112301 ◽  
Author(s):  
J. Ablinger ◽  
J. Blümlein ◽  
C. G. Raab ◽  
C. Schneider
Keyword(s):  
Iterated Integrals ◽  
Binomial Sums

scholarly journals Nested (inverse) binomial sums and new iterated integrals for massive Feynman diagrams

2014 ◽  
Author(s):  
Clemens Gunter Raab ◽  
Jakob Ablinger ◽  
Johannes Bluemlein ◽  
Carsten Schneider
Keyword(s):  
Feynman Diagrams ◽  
Iterated Integrals ◽  
Binomial Sums

scholarly journals Master integrals for bipartite cuts of three-loop photon self energy

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
R. N. Lee ◽  
A. I. Onishchenko
Keyword(s):  
Spectral Density ◽  
High Energy ◽  
Elliptic Integrals ◽  
Iterated Integrals ◽  
Self Energy ◽  
Complete Elliptic Integrals ◽  
The One

Abstract We calculate the master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals, which, apart from the 4m cut (the cut of 4 massive lines), reduce to Goncharov’s polylogarithms. The master integrals for 4m cut have been calculated in our previous paper in terms of the one-fold integrals of harmonic polylogarithms and complete elliptic integrals. We provide the threshold and high-energy asymptotics of the master integrals found, including those for 4m cut.

scholarly journals Three-loop contributions to the ρ parameter and iterated integrals of modular forms

2020 ◽  
Vol 2020 (2) ◽  
Author(s):  
Samuel Abreu ◽  
Matteo Becchetti ◽  
Claude Duhr ◽  
Robin Marzucca
Keyword(s):  
Modular Forms ◽  
Iterated Integrals

scholarly journals Elliptic polylogarithms and iterated integrals on elliptic curves. Part I: general formalism

2018 ◽  
Vol 2018 (5) ◽  
Author(s):  
Johannes Broedel ◽  
Claude Duhr ◽  
Falko Dulat ◽  
Lorenzo Tancredi
Keyword(s):  
Elliptic Curves ◽  
Iterated Integrals
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