Related papers: Evaluation of integrals by differentiation with re…
We propose a novel method for fast and scalable evaluation of periodic solutions of systems of ordinary differential equations for a given set of parameter values and initial conditions. The equations governing the system dynamics are…
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…
We show that integro-differential generalized Langevin and non-Markovian master equations can be transformed into larger sets of ordinary differential equations. .On the basis of this transformation we develop a numerical method for solving…
The automated analysis of administrative documents is an important field in document recognition that is studied for decades. Invoices are key documents among these huge amounts of documents available in companies and public services.…
We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…
Interpreting data with mathematical models is an important aspect of real-world industrial and applied mathematical modeling. Often we are interested to understand the extent to which a particular set of data informs and constrains model…
We give necessary and sufficient conditions for differentiating under the integral sign an integral that depends on a parameter. The conditions require the equality of two iterated integrals and depend on being able to integrate every…
In this article, we introduce the parametrix technique in order to construct fundamental solutions as a general method based on semigroups and their generators. This leads to a probabilistic interpretation of the parametrix method that is…
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
The problem of quantizing theories defined over configuration spaces described by non-commuting parameters is considered. In this paper we describe the first step in this direction, that is the definition of an integral over a general…
We present a methodology for numerically integrating ordinary differential equations containing rapidly oscillatory terms. This challenge is distinct from that for differential equations which have rapidly oscillatory solutions: here the…
Path integrals are a ubiquitous tool in theoretical physics. However, their use is sometimes hindered by the lack of control on various manipulations -- such as performing a change of the integration path -- one would like to carry out in…
The theory of Lie remarkable equations, i.e. differential equations characterized by their Lie point symmetries, is reviewed and applied to ordinary differential equations. In particular, we consider some relevant Lie algebras of vector…
In this work, we introduce a new generalized integral transform involving many potentially known or new transforms as special cases. Basic properties of the new integral transform, that investigated in this work, include the existence…
Using elementary methods, we define and derive a particular weighted average of the trapezoidal and composite trapezoidal rules and show that this approximation, as well as its composite, is straightforward in computation. This…
The method for analytic evaluation of four-particle integrals, proposed by Fromm and Hill, is generalized to include complex exponential parameters. An original procedure of numerical branch tracking for multiple valued functions is…
In the present article, the author uses Fourier theory of tempered distributions (generalized functions) in deriving a formula for Dirichlet-like integrals. The applied method is remarkably efficient and allows a solution in a few…
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques…
All integrals available in literature and books, that are related to Sinc(=sin x/x) function, are special cases of the general form of the integral given in the title. The evaluation of the integral is divided into two cases (i) $a$ and $b$…