Related papers: Inverse Mellin Transform of Holonomic Sequences
Discrete analogs of the index transforms, involving Bessel and the modified Bessel functions are introduced and investigated. The corresponding inversion theorems for suitable classes of functions and sequences are established.
Quantum hamiltonian reduction is a fundamental tool of conformal field theory and vertex algebra representation theory. It has traditionally been applied to study highest-weight modules. On the other hand, inverse quantum hamiltonian…
We present several sequences involving harmonic numbers and the central binomial coefficients. The calculational technique is consists of a special summation method that allows, based on proper two-valued integer functions, to calculate…
An analytical-numeric calculation method of extremely complicated integrals is presented. These integrals appear often in magnet soliton theory. The appropriate analytical continuation and a corresponding integration contour allow to reduce…
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…
Given a permutation polynomial of a large finite field, finding its inverse is usually a hard problem. Based on a piecewise interpolation formula, we construct the inverses of cyclotomic mapping permutation polynomials of arbitrary finite…
A new approach to compute Feynman Integrals is presented. It relies on an integral representation of a given Feynman Integral in terms of simpler ones. Using this approach, we present, for the first time, results for a certain family of…
The Lorentz Integral Transform approach allows microscopic calculations of electromagnetic reaction cross sections without explicit knowledge of final state wave functions. The necessary inversion of the transform has to be treated with…
We give presentation of composition inverse of formal power serie in a logarithmic form.
A new strategy based on numerical homogenization and Bayesian techniques for solving multiscale inverse problems is introduced. We consider a class of elliptic problems which vary at a microscopic scale, and we aim at recovering the highly…
The accuracy of reconstruction of a response function from its Lorentz integral transform is studied in an exactly solvable model. An inversion procedure is elaborated in detail and features of the procedure are studied. Unlike results in…
An ill-defined integral equation for modeling the mass-spectrum of mesons is regulated with an additional but unphysical parameter. This parameter dependance is removed by renormalization. Illustrative graphical examples are given.
We derive the algebraic relations of alternating and non-alternating finite harmonic sums up to the sums of depth~6. All relations for the sums up to weight~6 are given in explicit form. These relations depend on the structure of the index…
In this paper we study the inverse Laplace transform. We first derive a new global logarithmic stability estimate that shows that the inversion is severely ill-posed. Then we propose a regularization method to compute the inverse Laplace…
Sequence transformations are important tools for the convergence acceleration of slowly convergent scalar sequences or series and for the summation of divergent series. Transformations that depend not only on the sequence elements or…
We introduce techniques to treat numerically Mellin-Barnes integrals in physical regions, which arise in the need of the computation of Feynman integrals for the electroweak two-loop corrections to the pseudo observables at the Z-boson…
We investigate Mellin integrals of products of hyperplanes, raised to an individual power each. We refer to the resulting functions as combinatorial correlators. We investigate their behavior when moving the hyperplanes individually. To…
Broadband hyperspectral digital holography and Fourier transform spectroscopy are important instruments in various science and application fields. In the digital hyperspectral holography and spectroscopy the variable of interest are…
Slowly convergent or divergent sequences and series occur abundantly in quantum physics and quantum chemistry. These convergence problems can be overcome with the help of nonlinear sequence transformations (Wynn's epsilon or rho algorithm,…
We solve exactly the scalar box integral using the Mellin-Barnes representation. Firstly we recognize the hypergeometric functions resumming the series coming from the scalar integrals, then we perform an analytic continuation before…