Related papers: Analytic Continuation of Mellin Transforms up to t…
We develop the technique of inverse Mellin transform for processes occurring in a background magnetic field. We show by analyticity that the energy (momentum) derivatives of a field theory amplitude at the zero energy (momentum) is equal to…
In this article, $q$-regular sequences in the sense of Allouche and Shallit are analysed asymptotically. It is shown that the summatory function of a regular sequence can asymptotically be decomposed as a finite sum of periodic fluctuations…
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 present an overview of fractional analytic QCD beyond leading order, following the results recently obtained in Ref. [1]. We demonstrate four different representations, the details of their derivation, and show the applicability of…
The compound models of clutter statistics are found suitable to describe the nonstationary nature of radar backscattering from high-resolution observations. In this letter, we show that the properties of Mellin transform can be utilized to…
We report a new result for the $N_f \,C_F^3$ contribution to the four-loop anomalous dimensions of non-singlet, twist-two operators in Quantum Chromodynamics. This result is obtained through computations of off-shell operator matrix…
We calculate the full set of the two-loop master integrals for heavy-to-light form factors of two different massive fermions for arbitrary momentum transfer in NNLO QCD or QED corrections. These integrals allow to determine the two-loop QCD…
A multiple Dirichlet series in two variables is constructed as a Mellin transform of a higher order Eisenstein series. It is shown to extend to a meromorphic function and satisfy two independent functional equations.
In the framework of analytic approach to QCD the nonperturbative contributions in running coupling of strong interaction up to 4-loop order are obtained in an explicit form. For all $Q>\Lambda$ they are shown to be represented in the form…
In this note we show that for an arbitrary semisimple Lie group and any admissible irreducible Banach representation the Mellin transforms of Whittaker functions extend to meromorphic functions. We locate the possible poles.
This paper deals with Mellin transforms of rational functions $g/f$ in several variables. We prove that the polar set of such a Mellin transform consists of finitely many families of parallel hyperplanes, with all planes in each such family…
The QCD analytic running coupling alpha_{an} which has no nonphysical singularities for all Q^2>0 is considered for the initial perturbation theory approximations up to four loop order. The finiteness of the analytic coupling at zero is…
The modified Mellin transform ${\cal Z}_k(s) = \int_1^\infty |\zeta({1\over2}+ix|^{2k}x^{-s}{\rm d} x$ ($k\ge1$ is a fixed integer, $s = \sigma + it$) is used to obtain estimates for $$…
We study the fixed point for a non-linear transformation in the set of Hausdorff moment sequences, defined by the formula: $T((a_n))_n=1/(a_0+... +a_n)$. We determine the corresponding measure $\mu$, which has an increasing and convex…
We have derived the coefficients of the highest three 1/x-enhanced small-x logarithms of all timelike splitting functions and the coefficient functions for the transverse fragmentation function in one-particle inclusive e^+e^- annihilation…
In this article, the infinite series form of the probability densities of tempered stable and inverse tempered stable subordinators are obtained using Mellin transform. Further, the densities of the products and quotients of stable and…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
Functional integrals are defined in terms of locally compact topological groups and their associated Banach-valued Haar integrals. This approach generalizes the functional integral scheme of Cartier and DeWitt-Morette. The definition allows…
We introduce an analytic function $\Psi(s_1,\ldots,s_r;w)$ that interpolates truncated multiple zeta functions $\zeta_N(s_1,\ldots,s_r)$. We represent this interpolant as a Mellin transform of a function $G(q_1,\ldots,q_r;w)$ and, using…
We construct the Mellin representation of four point conformal correlation function with external primary operators with arbitrary integer spacetime spins, and obtain a natural proposal for spinning Mellin amplitudes. By restricting to the…