• Corpus ID: 54612597

Counting master integrals: Integration by parts vs. functional equations

@article{Kniehl2016CountingMI,
  title={Counting master integrals: Integration by parts vs. functional equations},
  author={Bernd A. Kniehl and O. V. Tarasov},
  journal={arXiv: High Energy Physics - Theory},
  year={2016}
}
We illustrate the usefulness of functional equations in establishing relationships between master integrals under the integration-by-parts reduction procedure by considering a certain two-loop propagator-type diagram as an example. 
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References

SHOWING 1-10 OF 31 REFERENCES
Counting master integrals: Integration by parts vs. differential reduction
Counting master integrals: integration-by-parts procedure with effective mass
A theorem on analytical calculability of 4-loop renormalization group functions
Functional equations for Feynman integrals
New types of equations for Feynman integrals are found. It is shown that the latter satisfy functional equations that relate integrals with different kinematics. A regular method for obtaining such…
Differential Reduction Algorithms for Hypergeometric Functions Applied to Feynman Diagram Calculation
We describe the application of differential reduction algorithms for Feynman Diagram calculation. We illustrate the procedure in the context of generalized hypergeometric functions, and give an…
Generalized recurrence relations for two-loop propagator integrals with arbitrary masses
Mellin-Barnes representations of Feynman diagrams, linear systems of differential equations, and polynomial solutions
Differential Reduction Techniques for the Evaluation of Feynman Diagrams
Stable reduction methods will be important in the evaluation of high-order perturbative diagrams appearing in QCD and mixed QCD-electroweak radiative corrections at the LHC. Differential reduction…
“Sixth root of unity” and Feynman diagrams: hypergeometric function approach point of view
Feynman Diagrams, Differential Reduction, and Hypergeometric Functions
We will present some (formal) arguments that any Feynman diagram can be understood as a particular case of a Horn-type multivariable hypergeometric function. The advantages and disadvantages of this…
...
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4
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