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Related papers: Mellin-Barnes and the method of brackets

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The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the…

Classical Analysis and ODEs · Mathematics 2017-07-28 Ivan Gonzalez , Karen Kohl , Lin Jiu , Victor H. Moll

A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for theevaluation of Feynman diagrams. We describe the operational rules and illustrate the method…

Mathematical Physics · Physics 2008-12-18 Ivan Gonzalez , Victor H. Moll

A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for the evaluation of Feynman diagrams. The operational rules are described and the method is…

Mathematical Physics · Physics 2010-04-14 Ivan Gonzalez , Victor H. Moll , Armin Straub

The method of brackets is an procedure to evaluate definite integrals. It is based on a small number of operational rules. The flexibility of this method is illustrated with the evaluation of an integral involving the Bessel K0 function and…

Classical Analysis and ODEs · Mathematics 2024-01-02 Ivan Gonzalez , John Lopez Santander , Victor H. Moll

In this paper, we present a new approach to the construction of Mellin-Barnes representations for Feynman integrals inspired by the Method of Brackets. The novel technique is helpful to lower the dimensionality of Mellin-Barnes…

High Energy Physics - Phenomenology · Physics 2017-09-13 Mario Prausa

The method of brackets is a method of integration based upon a small number of heuristic rules. Some of these have been made rigorous. An example of an integral involving the Bessel function is used to motivate a new evaluation rule.

Classical Analysis and ODEs · Mathematics 2017-05-11 Ivan Gonzalez , Lin Jiu , Victor H. Moll

The Method of Brackets (MoB) is a technique used to compute definite integrals, that has its origin in the negative dimensional integration method. It was originally proposed for the evaluation of Feynman integrals for which, when…

High Energy Physics - Theory · Physics 2021-12-20 B. Ananthanarayan , Sumit Banik , Samuel Friot , Tanay Pathak

The method of brackets, consisting of a small number of heuristic rules, was created by Ivan Gonzalez for the evaluation of definite integrals appearing in the resolution of Feynman diagrams. The current work verifies each step of this…

Classical Analysis and ODEs · Mathematics 2017-10-11 Lin Jiu

Some recent results on evaluating Feynman integrals are reviewed. The status of the method based on Mellin-Barnes representation as a powerful tool to evaluate individual Feynman integrals is characterized. A new method based on Groebner…

High Energy Physics - Phenomenology · Physics 2009-11-11 V. A. Smirnov

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the…

High Energy Physics - Phenomenology · Physics 2014-11-20 Ayres Freitas , Yi-Cheng Huang

In this work we present the relation between method of brackets and the master theorem of Ramanujan in the evaluation of multivariable integrals, in this case Feynman diagrams.

High Energy Physics - Theory · Physics 2015-05-19 Iván González

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…

Mathematical Physics · Physics 2015-05-28 Samuel Friot , David Greynat

We present new closed-form expressions for certain improper integrals of Mathematical Physics such as certain Ising, Box, and Associated integrals. The techniques we employ here include (a) the Method of Brackets and its modifications and…

Mathematical Physics · Physics 2024-02-05 B. Ananthanarayan , Tanay Pathak , Kartik Sharma

We use the method of brackets to evaluate quadratic and quartic type integrals. We recall the operational rules of the method and give examples to illustrate its working. The method is then used to evaluate the quadratic type integrals…

Mathematical Physics · Physics 2019-09-04 B Ananthanarayan , Sumit Banik , Sudeepan Datta , Tanay Pathak

Two recently developed techniques of analytic evaluation of multifold Mellin-Barnes (MB) integrals are presented. Both approaches rest on the definition of geometrical objets conveniently associated with the MB integrands, which can then be…

High Energy Physics - Theory · Physics 2024-02-07 Sumit Banik , Samuel Friot

The status of analytical evaluation of double and triple box diagrams is characterized. The method of Mellin-Barnes representation as a tool to evaluate master integrals in these problems is advocated. New MB representations for massive…

High Energy Physics - Phenomenology · Physics 2009-11-10 V. A. Smirnov

In this paper we provide a unified approach to a family of integrals of Mellin--Barnes type using distribution theory and Fourier transforms. Interesting features arise in many of the cases which call for the application of pull-backs of…

Classical Analysis and ODEs · Mathematics 2012-08-31 Gopala Krishna Srinivasan

This article is written with the hope to draw attention to a method that uses integral transforms to find exact values for a large class of convergent series (and, in particular, series of rational terms). We apply the method to some series…

Classical Analysis and ODEs · Mathematics 2007-10-08 Costas J. Efthimiou

Mellin-Barnes (MB) integrals are well-known objects appearing in many branches of mathematics and physics, ranging from hypergeometric functions theory to quantum field theory, solid state physics, asymptotic theory, etc. Although MB…

High Energy Physics - Theory · Physics 2021-10-13 B. Ananthanarayan , Sumit Banik , Samuel Friot , Shayan Ghosh

One of the two existing strategies of resolving singularities of multifold Mellin-Barnes integrals in the dimensional regularization parameter, or a parameter of the analytic regularization, is formulated in a modified form. The…

High Energy Physics - Phenomenology · Physics 2009-07-24 A. V. Smirnov , V. A. Smirnov
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