2012
DOI: 10.1063/1.3679686
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On convergent series representations of Mellin-Barnes integrals

Abstract: Multiple Mellin-Barnes integrals are often used for perturbative calculations in particle physics. In this context, the evaluation of such objects may be performed through residues calculations which lead to their expression as multiple series in powers and logarithms of the parameters involved in the problem under consideration. However, in most of the cases, several series representations exist for a given integral. They converge in different regions of values of the parameters, and it is not obvious to obta… Show more

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Cited by 37 publications
(36 citation statements)
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“…To compute this integral one can directly apply the general method described in [Friot-Greynat (2012)]. If one follows this approach, one will find three double series representations (one of them being the one mentioned in [Ruby (1994)] and studied in [Pommé (2004)]), converging in three different regions of values of the parameters R S , R D and d.…”
Section: Ruby's Formulamentioning
confidence: 99%
See 1 more Smart Citation
“…To compute this integral one can directly apply the general method described in [Friot-Greynat (2012)]. If one follows this approach, one will find three double series representations (one of them being the one mentioned in [Ruby (1994)] and studied in [Pommé (2004)]), converging in three different regions of values of the parameters R S , R D and d.…”
Section: Ruby's Formulamentioning
confidence: 99%
“…The real power of the MB method rests on the fact that, for a large class of MB integrals, we still would have been able to obtain several series representations, analytic continuations of each other, following the method presented in [Friot-Greynat (2012)]. …”
mentioning
confidence: 99%
“…[22] (see also refs. [23,24,25] for applications in QED). This theorem relates the singularities in the complex s-plane of the integrand, i.e.…”
Section: The Hadronic Vacuum Polarization Two-point Functionmentioning
confidence: 99%
“…In case of multiple Mellin-Barnes parameters, results from the theory of several complex variables may have to be used for analytic evaluation [39].…”
Section: The Mellin-barnes Methodsmentioning
confidence: 99%