Using functional equations to calculate Feynman integrals

DOI10.1134/S0040577919080129zbMath1431.81062OpenAlexW2971589683MaRDI QIDQ2286423

Oleg V. Tarasov

Publication date: 22 January 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577919080129

zbMATH Keywords

functional equationhypergeometric functionFeynman integral

Mathematics Subject Classification ID

Feynman diagrams (81T18) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30) Classical hypergeometric functions, ({}_2F_1) (33C05) General theory of functional equations and inequalities (39B05)

Related Items (8)

Analytic continuation of the Kampé de Fériet function and the general double Horn series ⋮ Analytic continuation of Lauricella's function F_D^(N) for large in modulo variables near hyperplanes {z_j = z_l} ⋮ Formulas for analytic continuation of Horn functions of two variables ⋮ Analytic continuation of Lauricella's function F_D^(N) for variables close to unit near hyperplanes {z_j = z_l} ⋮ \texttt{AlgRel.wl}: algebraic relations for the product of propagators in Feynman integrals ⋮ Constructing basises in solution space of the system of equations for the Lauricella Function F _D ^(N) ⋮ Formulas for computing the Lauricella function in the case of crowding of variables ⋮ Horn's hypergeometric functions with three variables

Uses Software

• Hypexp
• pySecDec

Cites Work

• Hypexp, a Mathematica package for expanding hypergeometric functions around integer-valued parameters
• Algebraic reduction of one-loop Feynman graph amplitudes
• IR finite one-loop box scalar integral with massless internal lines
• Analytic continuation of the Appell function \(F_1\) and integration of the associated system of equations in the logarithmic case
• Derivation of functional equations for Feynman integrals from algebraic relations
• Functional equations in applied sciences
• HIGH-PRECISION CALCULATION OF MULTILOOP FEYNMAN INTEGRALS BY DIFFERENCE EQUATIONS
• Some exact results for N-point massive Feynman integrals
• Connection between Feynman integrals having different values of the space-time dimension
• Integration of the Partial Differential Equations for the Hypergeometric Functions F1 and FD of Two and More Variables
• Functional equations and how to solve them
• pySecDec: a toolbox for the numerical evaluation of multi-scale integrals
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