## Solving differential equations for Feynman integrals by expansions near singular points.(English)Zbl 1388.81927

Summary: We describe a strategy to solve differential equations for Feynman integrals by powers series expansions near singular points and to obtain high precision results for the corresponding master integrals. We consider Feynman integrals with two scales, i.e. non-trivially depending on one variable. The corresponding algorithm is oriented at situations where canonical form of the differential equations is impossible. We provide a computer code constructed with the help of our algorithm for a simple example of four-loop generalized sunset integrals with three equal non-zero masses and two zero masses. Our code gives values of the master integrals at any given point on the real axis with a required accuracy and a given order of expansion in the regularization parameter $$\epsilon$$.

### MSC:

 81V05 Strong interaction, including quantum chromodynamics 81U05 $$2$$-body potential quantum scattering theory 81Q30 Feynman integrals and graphs; applications of algebraic topology and algebraic geometry

### Keywords:

Feynman integral; scattering amplitudes; perturbative QCD

### Software:

HPL; FIRE5; LiteRed; GiNaC; epsilon; FIRE; sunem; Fuchsia
Full Text:

### References:

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