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We present a set of Feynman integrals appearing in calculations of different QED processes to the one-loop accuracy. We consider scalar, vector, and tensor integrals with two, three, four and five denominators. The cases of equal and…
Let $\overline{N}_2(a,c,n)$ be the number of overpartitions of $n$ whose the $M_2$-rank is congruent to $a$ modulo $c$. In this paper, we obtain the asymptotic formula of $\overline{N}_2(a,c,n)$ utilizing the Ingham Tauberian Theorem. As…
In previous work of C. A. Tracy and the author asymptotic formulas were derived for certain operator determinants whose interest lay in the fact that quotients of them gave solutions to the cylindrical Toda equations. In the present paper…
We derive the QCD corrections to the electroweak gauge bosons vacuum polarization functions at high and zero--momentum transfer in the case of arbitrary internal quark masses. We then discuss in this general case (i) the connection between…
We study the asymptotic behavior of the counting function of tensor products of operators, in the cases where the factors are either pseudodifferential operators on closed manifolds, or pseudodifferential operators of Shubin type on…
In this paper we derive non-classical Tauberian asymptotic at infinity for the tail, the density and the derivatives thereof of a large class of exponential functionals of subordinators. More precisely, we consider the case when the L\'evy…
We prove Central Limit Theorems and Stein-like bounds for the asymptotic behaviour of nonlinear functionals of spherical Gaussian eigenfunctions. Our investigation combine asymptotic analysis of higher order moments for Legendre polynomials…
Let $K_\lambda^d$ be the convex hull of the intersection of the homogeneous Poisson point process of intensity $\lambda$ in $\mathbb{R}^d$, $d \ge 2$, with the Euclidean unit ball $\mathbb{B}^d$. In this paper, we study the asymptotic…
A systematic study of the scalar one-loop two-, three-, and four-point Feynman integrals is performed. We consider all cases of mass assignment and external invariants and derive closed expressions in arbitrary space-time dimension in terms…
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications…
In this paper we consider the strong asymptotic behavior of Laguerre polynomials in the complex plane. The leading behavior is well known from Perron and Mehler-Heine formulas, but higher order coefficients, which are important in the…
We study the Fourier transform of polynomials in an orthogonal family, taken with respect to the orthogonality measure. Mastering the asymptotic properties of these transforms, that we call Fourier--Bessel functions, in the argument, the…
We provide a complete combinatorial and asymptotic analysis of positive linear systems of equations in one catalytic variable that appear in several combinatorial problems such as in lattice path counting or stack-sortable permutation…
We consider processes which produce final state hadrons whose energy is much greater than their mass. In this limit interactions involving collinear fermions and gluons are constrained by a symmetry, and we give a general set of rules for…
In this paper we compute some of the higher order terms in the large-t asymptotic expansion of the Airy process two-point function, extending the previous work of Adler and van Moerbeke and Widom. We prove that it is possible to represent…
We derive the low-temperature large-distance asymptotics of the transversal two-point functions of the XXZ chain by summing up the asymptotically dominant terms of their expansion into form factors of the quantum transfer matrix. Our…
The problem is a power-law asymptotics of the probability that a self-similar process does not exceed a fixed level during long time. The exponent in such asymptotics is estimated for some Gaussian processes, including the fractional…
We develop perturbative QCD formalism for three-body nonleptonic $B$ meson decays. Leading contributions are identified by defining power counting rules for various topologies of amplitudes. The analysis is simplified into the one for…
This paper considers the asymptotic behaviour of deterministically and stochastically forced linear pantograph equations. The asymptotic behaviour is studied in the case when all solutions of the pantograph equation without forcing tend to…
We identify and evaluate a class of physical amplitudes in four-dimensional N=4 superstring theory, which receive, in the weak coupling limit, contributions of order e^{-1/\lambda}, where \lambda is the type II superstring coupling…