The system of partial differential equations for the $C_{{}_0}$ function

Abstract

We present an approach to analyze the scalar integrals of any Feynman diagrams in detail here. This method not only completely recovers some well-known results in the literature, but also produces some brand new results on the $C_{{}_0}$ function. The approach can be employed to evaluate the coefficient of arbitrary power of $\epsilon$ in the expansion of a scalar integral, where $D=4-2\epsilon$ denotes the time-space dimension.

Latex, 68 pages

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• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
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• Evaluating Feynman integrals by the hypergeometry

Cited by in corpus (9)

• GKZ-hypergeometric systems for Feynman integrals
• $\epsilon$-Expansion of Multivariable Hypergeometric Functions Appearing in Feynman Integral Calculus
• Analytic continuations and numerical evaluation of the Appell $F_1$, $F_3$, Lauricella $F_D^{(3)}$ and Lauricella-Saran $F_S^{(3)}$ and their Application to Feynman Integrals
• Analytic continuations of the Horn $H_1$ and $H_5$ functions
• GKZ-system of the 2-loop self energy with 4 propagators
• Feynman Integrals of Grassmannians
• GKZ hypergeometric systems of the three-loop vacuum Feynman integrals
• The four-propagator three-loop vacuum integral by the hypergeometry
• GKZ hypergeometric systems of the four-loop vacuum Feynman integrals