Related papers: On evaluation of integrals involving Bessel functi…
I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
We review the Laporta algorithm for the reduction of scalar integrals to the master integrals and the differential equations technique for their evaluation. We discuss the use of the basis of harmonic polylogarithms for the analytical…
Based on the Baikov representation, we present a systematic approach to compute cuts of Feynman Integrals, appropriately defined in $d$ dimensions. The information provided by these computations may be used to determine the class of…
When treating problems of vector diffraction in electromagnetic theory, the evaluation of the integral involving Bessel and associated Legendre functions is necessary. Here we present the analytical result for this integral that will make…
A purely numerical method, Direct ComputationMethod is applied to evaluate Feynman integrals. This method is based on the combination of an efficient numerical integration and an efficient extrapolation. In addition, high-precision…
We derive new approximate representations of the Lommel functions in terms of the Scorer function and approximate representations of the first derivative of the Lommel functions in terms of the derivative of the Scorer function. Using the…
In this work, series expansions in terms of Bessel functions of the first kind are given for the sine and cosine integrals. These representations differ from many of the known Neumann-type series expansions for the sine and cosine…
A prototype for an extensible interactive graphical term manipulation system is presented that combines pattern matching and nondeterministic evaluation to provide a convenient framework for doing tedious algebraic manipulations that so far…
An umbral type formalism is used to derive integrals involving products of Laguerre polynomials and other special functions.
We investigate a family of integrals involving modified Bessel functions that arise in the context of neutrino scattering. Recursive formulas are derived for evaluating these integrals and their asymptotic expansions are computed. We prove…
This is a review paper of recent results in the perturbative symmetry approach in the symbolic representation.
Discrete analogs of the Lebedev transforms with the product of the modified Bessel functions are introduced and investigated. Several expansions of suitable functions and sequences in terms of the series and integrals, involving the…
The moments of Bessel functions and Bessel-trigonometric functions play a basic role in many practical problems and numerical analysis. This paper presents a complete analysis for these moments based on the recursive relations of Bessel…
This talk summarizes recent developments in the evaluation of Feynman integrals using hyperlogarithms. We discuss extensions of the original method, new results that were obtained with this approach and point out current problems and future…
Analytical formulas for some useful three-particles integrals are derived. Many of these integrals include Bessel and/or trigonometric functions of one and two interparticle (relative) coordinates $r_{32}, r_{31}$ and $r_{21}$. The formulas…
For the investigation of higher order Feynman integrals, potentially with tensor structure, it is highly desirable to have numerical methods and automated tools for dedicated, but sufficiently 'simple' numerical approaches. We elaborate two…
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials into a "different" mathematical language. The language we…
A big class of Feynman integrals, in particular, the coefficients of their Laurent series expansion w.r.t.\ the dimension parameter $\ep$ can be transformed to multi-sums over hypergeometric terms and harmonic sums. In this article, we…
A symbolic method for solving linear recurrences of combinatorial and statistical interest is introduced. This method essentially relies on a representation of polynomial sequences as moments of a symbol that looks as the framework of a…