Related papers: Explicit solutions of the multi-loop integral recu…
We study a two-loop contribution to the dark-matter trispectrum and evaluate it numerically using an infrared-safe integrand. The calculation is organized as an expansion around a fixed reference cosmology: the linear matter power spectrum…
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…
In this paper we give efficient algorithms for computing second-, third-, and fourth-order linear recurrences. We also present an algorithm scheme for computing terms with the indices $N,\ldots,N+n-1$ of an $n$th-order linear recurrence.…
We introduce a class of iterated integrals, defined through a set of linearly independent integration kernels on elliptic curves. As a direct generalisation of multiple polylogarithms, we construct our set of integration kernels ensuring…
We study the problem of solving integration-by-parts recurrence relations for a given class of Feynman integrals which is characterized by an arbitrary polynomial in the numerator and arbitrary integer powers of propagators, {\it i.e.}, the…
We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals…
In the standard perturbation theory (SPT) of self-gravitating Newtonian fluid in an expanding universe, recurrence relations for higher-order solutions are well known and play an important role both in practical applications and in…
We calculate analytically the three-loop planar master integrals relevant for heavy-to-light form factors using the method of differential equations. After choosing a proper canonical basis, the boundary conditions are easy to be…
Centered finite volume methods are considered in the context of Numerical Relativity. A specific formulation is presented, in which third-order space accuracy is reached by using a piecewise-linear reconstruction. This formulation can be…
We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield…
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…
Repeated integration is a major topic of integral calculus. In this article, we study repeated integration. In particular, we study repeated integrals and recurrent integrals. For each of these integrals, we develop reduction formulae for…
Power series in which the summand satisfies a linear recurrence relation with polynomial coefficients are shown to be the solution of a linear differential or algebraic equation. Solving the associated differential or algebraic equation…
The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the…
Finding correspondences between shapes is a fundamental problem in computer vision and graphics, which is relevant for many applications, including 3D reconstruction, object tracking, and style transfer. The vast majority of correspondence…
We give a short proof of polynomial recurrence with large intersection for additive actions of finite-dimensional vector spaces over countable fields on probability spaces, improving upon the known size and structure of the set of strong…
Recently the authors and J.M. Kress presented a special function recurrence relation method to prove quantum superintegrability of an integrable 2D system that included explicit constructions of higher order symmetries and the structure…
We give a definition of higher dimensional iterated integrals based on integration over membranes. We prove basic properties of this definition and formulate a conjecture which extends Chen's de Rham Theorem for iterated integrals to the…
Explicitly-correlated F12 methods are becoming the first choice for high-accuracy molecular orbital calculations, and can often achieve chemical accuracy with relatively small gaussian basis sets. In most calculations, the many three- and…
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…