Related papers: Quadratic and quartic integrals using the method o…
The method of brackets is an efficient method for the evaluation of a large class of definite integrals on the half-line. It is based on a small collection of rules, some of which are heuristic. The extension discussed here is based on the…
A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for theevaluation of Feynman diagrams. We describe the operational rules and illustrate the method…
A new heuristic method for the evaluation of definite integrals is presented. This method of brackets has its origin in methods developed for the evaluation of Feynman diagrams. The operational rules are described and the method is…
We review a special technique for evaluating challenging integrals by providing a number of examples. Many of our examples prove integrals from the popular table of Gradshteyn and Ryzhik.
The method of brackets is an procedure to evaluate definite integrals. It is based on a small number of operational rules. The flexibility of this method is illustrated with the evaluation of an integral involving the Bessel K0 function and…
The method of brackets is a method for the evaluation of definite integrals based on a small number of rules. This is employed here for the evaluation of Mellin-Barnes integral. The fundamental idea is to transform these integral…
The table of Gradshteyn and Rhyzik contains some trigonometric integrals that can be expressed in terms of the beta function. We describe the evaluation of some of them.
The well known table of Gradshteyn and Ryzhik contains indefinite and definite integrals of both elementary and special functions. We give proofs of several entries containing integrands with some combination of hyperbolic and trigonometric…
The table of Gradshteyn and Ryzhik contains many entries that are related to elliptic integrals. We present a systematic derivation of some of them.
In this study, new master theorems and general formulas of integrals are presented and implemented to solve some complicated applications in different fields of science. The proposed theorems are considered to be generators of new problems,…
In this paper we study the set of values of quadratic form at points of a cut and project set. We will establish conditions which ensure that the set of values is dense. Our methods involve homogeneous dynamics and we will prove a orbit…
The classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik contains some elementary integrals. We discuss their evaluations.
The table of Gradshteyn and Ryzhik contains some integrals that can be reduced to the Frullani type. We present a selection of them.
A method of deriving quadrature rules has been developed which gives nodes and weights for a Gaussian-type rule which integrates functions of the form: f(x,y,t) = a(x,y,t)/((x-t)^2+y^2) + b(x,y,t)/([(x-t)^2+y^2]^{1/2}) +…
A method is presented for the analytical evaluation of the singular and near-singular integrals arising in the Boundary Element Method solution of the Helmholtz equation. An error analysis is presented for the numerical evaluation of such…
In this work derivations of definite integrals listed in Prudnikov volume I, Gradshteyn and Ryzhik and a few other tables are produced. Special cases of these integrals in terms of fundamental constants are also evaluated. The method used…
We show how the integral formula of Poisson for holomorphic functions on the right half plane can be used to quickly evaluate certain integrals from the Table of Gradshteyn and Ryzhik. In addition, we prove a version of this formula for…
An elementary proof of an entry in the table of integrals by Gradshteyn and Rhyzik is presented.
We investigate factorizability of a quadratic split quaternion polynomial. In addition to inequality conditions for existence of such factorization, we provide lucid geometric interpretations in the projective space over the split…
We prove several results about integers represented by positive definite quadratic forms, using a Fourier analysis approach. In particular, for an integer $\ell\geq 1$, we improve the error term in the partial sums of the number of…