Related papers: Counting master integrals: Integration by parts vs…
In this paper we provide a rigorous mathematical foundation for continuous approximations of a class of systems with piece-wise continuous functions. By using techniques from the theory of differential inclusions, the underlying piece-wise…
We calculate master integrals for bipartite cuts of the three-loop propagator QED diagrams. These master integrals determine the spectral density of the photon self energy. Our results are expressed in terms of the iterated integrals,…
We consider the ratio of two Gauss hypergeometric functions, in which the parameters of the numerator function differ from the respective parameters of the denominator function by integers. We derive explicit integral representations for…
We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to…
We present numerical results which are needed to evaluate all non-trivial master integrals for four-loop massless propagators, confirming the recent analytic results of[1]and evaluating an extra order in $\ep$ expansion for each master…
We present a new formulation of the loop-tree duality theorem for higher loop diagrams valid both for massless and massive cases. $l$-loop integrals are expressed as weighted sum of trees obtained from cutting $l$ internal propagators of…
Two approximations, derived from continuous expansions of Riemann-Liouville fractional derivatives into series involving integer order derivatives, are studied. Using those series, one can formally transform any problem that contains…
In this work, we study the computation of reduction coefficients for multi loop Feynman integrals using generating functions constructed within the Baikov representation. Compared with traditional Feynman rules, the Baikov formalism offers…
This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For…
In this article, we construct two-dimensional integrable and superintegrable sys- tems in terms of the master function formalism and relate them to Mielnik;s and Marquette;s construction in supersymmetric quantum mechanics. For two diferent…
We compute the master integrals for two-loop QCD corrections to quasi parton distribution functions (PDFs) in large momentum effective theory. Analytical results of the master integrals are derived using the method of differential…
We prove two types of functional equations for double series of Euler type with complex coefficients. The first one is a generalization of the functional equation for the Euler double zeta-function, proved in a former work of the…
In this paper an iterated function system on the space of distribution functions is built. The inverse problem is introduced and studied by convex optimization problems. Some applications of this method to approximation of distribution…
Within the functional calculi of Bochner-Phillips and Hirsch, we describe the operators of distributed order differentiation and integration as functions of the classical differentiation and integration operators respectively.
Functional equations methods are a fundamental part of the theory of Exactly Solvable Models in Statistical Mechanics and they are intimately connected with Baxter's concept of commuting transfer matrices. This concept has culminated in the…
In this paper we introduce a new mathematical tool to solve fractional equations representing models of fractional systems : The Ultradistributions. Ultradistributions permit us to unify the notion of integral and derivative in one only…
The main goal of this research is to develop the concepts of a revolutionary processor system called Functional Processor System. The fairly novel work carried out in this proposal concentrates on decoding of function pipelines and…
Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.
We consider solvable matrix models. We generalize Harish-Chandra-Itzykson-Zuber and certain other integrals (Gross-Witten integral and integrals over complex matrices) using the notion of tau function of matrix argument. In this case one…
Properties of partial integrals such as real and complex-valued polynomial, multiple polynomial, exponential, and conditional for ordinary differential systems are studied. The possibilities of constructing first integrals and last…