Related papers: Explicit solutions of the 3--loop vacuum integral …

A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of…

We derive some q-analogs of Euler-Cassini-type identities and of recurrence formulas for powers of Fibonacci polynomials.

It is known that difference equations generated as the Newton-Raphson iteration for quadratic equations are solvable in closed form, and the solution can be constructed from linear three-term recurrence relations with constant coefficients.…

This paper reports several new classes of weakly unstable recurrent solutions of the 2+1-dimensional Euler equation on a square domain with periodic boundary conditions. These solutions have a number of remarkable properties which…

Linear differential equations and recurrences reveal many properties about their solutions. Therefore, these equations are well-suited for representing solutions and computing with special functions. We identify a large class of existing…

We revisit a model for three-dimensional, inviscid quasi-geostrophic flow on bounded, cylindrical domains introduced by the authors in \cite{nv18}. We prove the local-in-time existence of classical solutions.

This paper considers quadratic and super-quadratic reaction-diffusion systems for reversible chemistry, for which all species satisfy uniform-in-time $L^1$ a-priori estimates, for instance, as a consequence of suitable mass conservation…

In this paper we describe a new method of calculation of master integrals based on the solution of systems of difference equations in one variable. An explicit example is given, and the generalization to arbitrary diagrams is described. As…

A class of log-trigonometric integrals are evaluated in terms of elliptic functions. From this, by using the elliptic integral singular values, one can obtain closed form evaluations of integrals such as \[…

In this paper we propose a definition of a recurrence relation homomorphism and illustrate our definition with a few examples. We then define the period of a k-th order of linear recurrence relation and deduce certain preliminary results…

In this paper, we present a novel method to compute an explicit formula for the inverse of the confluent Vandermonde matrices. Our proposed results may have many interesting perspectives in diverse areas of mathematics and natural sciences,…

We derive recurrence relations for the calculation of multiloop sunset-type diagrams with large powers of massive propagators. The technique is formulated in configuration space and exploits the explicit form of the massive propagator…

The 3PI method is a technique to resum an infinite class of diagrams, which may be useful in studying nonperturbative thermodynamics and dynamics in quantum field theory. But it has never been successfully applied to gauge theories, where…

General algorithms for tensor reduction of two-loop massive vacuum diagrams are discussed. Some explicit useful formulae are presented.

In hep-th/9805025, a result for the symmetric 3-loop massive tetrahedron in 3 dimensions was found, using the lattice algorithm PSLQ. Here we give a more general formula, involving 3 distinct masses. A proof is devised, though it cannot be…

We first reformulate and expand with several novel findings some of the basic results in the integrability of Abel equations. Next, these results are applied to Vein's Abel equation whose solutions are expressed in terms of the third order…

We formulate a generic three-dimensional higher-derivative superfield theory for self-interacting scalar superfield action. We consider the cases of real and complex scalar superfields. For these theories, we explicitly calculate the…

We evaluate in closed form several classes of finite trigonometric sums. Two general methods are used. The first is new and involves sums of roots of unity. The second uses contour integration and extends a previous method used by two of…

A new approach is presented to evaluate multi-loop integrals, which appear in the calculation of cross-sections in high-energy physics. It relies on a fully numerical method and is applicable to a wide class of integrals with various mass…

Applications of a method recently suggested by one of the authors (R.L.) are presented. This method is based on the use of dimensional recurrence relations and analytic properties of Feynman integrals as functions of the parameter of…