Related papers: Expansion by regions meets angular integrals

A brief review of recent results on asymptotic expansions of Feynman integrals on the mass shell in momenta and masses and their application to 2-loop calculations is presented.

Asymptotic expansion of the wavelet transform for small values of the dilation parameter a is obtained using asymptotic expansion of the Mellin convolution technique ofWong. Asymptotic expansions of Morlet wavelet transform, Mexican hat…

Over the last several decades, improvements in the fields of analytic combinatorics and computer algebra have made determining the asymptotic behaviour of sequences satisfying linear recurrence relations with polynomial coefficients largely…

We consider the asymptotic behavior of the multidimensional Laplace-type integral with a perturbed phase function. Under suitable assumptions, we derive a higher-order asymptotic expansion with an error estimate, generalizing some previous…

Datasets from the fields of bioinformatics, chemometrics, and face recognition are typically characterized by small samples of high-dimensional data. Among the many variants of linear discriminant analysis that have been proposed in order…

We consider estimation procedures which are recursive in the sense that each successive estimator is obtained from the previous one by a simple adjustment. The model considered in the paper is very general as we do not impose any…

Asymptotic expansions for a wide class of distribution are studied. A simple method for computation of the series coefficients is suggested. The case when regularization parameter of the distribution depends on the asymptotic parameter is…

We construct asymptotic expansions for ordinary differential equations with highly oscillatory forcing terms, focussing on the case of multiple, non-commensurate frequencies. We derive an asymptotic expansion in inverse powers of the…

We compute angular phase-space integrals with three and four denominators analytically, working within dimensional regularisation via the Mellin-Barnes (MB) representation. The approach converts multifold MB integrals into real parametric…

Asymptotic expansion is presented for an estimator of the Hurst coefficient of a fractional Brownian motion. For this, a recently developed theory of asymptotic expansion of the distribution of Wiener functionals is applied. The effects of…

Integral means are important class of bivariate means. In this paper we prove the very general algorithm for calculation of coefficients in asymptotic expansion of integral mean. It is based on explicit solving the equation of the form…

This paper aims to derive explicit and computable error bounds for the asymptotic expansion of the Jacobi polynomials as their degree approaches infinity, using an integral method. The analysis focuses on the outer or oscillatory region of…

The growth-fragmentation equation describes a system of growing and dividing particles, and arises in models of cell division, protein polymerisation and even telecommunications protocols. Several important questions about the equation…

We study the boundary layer solution to singular perturbation problems involving Poisson-Boltzmann (PB) type equations with a small parameter $\epsilon$ in general bounded smooth domains (including multiply connected domains) under the…

We apply the method of regions to the massive two-loop integrals appearing in the Higgs pair production cross section at the next-to-leading order, in the high energy limit. For the non-planar integrals, a subtle problem arises because of…

Using distribution theory we present the moment asymptotic expansion of continuous wavelet transform in different distributional spaces for large and small values of dilation parameter $a$. We also obtain asymptotic expansions for certain…

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…

We analytically compute asymptotic expansions of a 1-dimensional sub-manifold of stable and unstable manifolds in a 4-dimensional symplectic mapping by using the method called asymptotic expansions beyond all orders. This method enables us…

This letter introduces a novel analytical approach to calculating phase-space integrals, crucial for precision in particle physics. We develop a method to compute angular components using multifold Mellin-Barnes integrals, yielding results…

We propose a form factor approach for the computation of the large distance asymptotic behavior of correlation functions in quantum critical (integrable) models. In the large distance regime we reduce the summation over all excited states…