Related papers: Exact Evaluation Of Some Highly Oscillatory Integr…
This paper deals with the evaluation of some definite Euler-type integrals in terms of the Wright hypergeometric function. We obtain a theorem on the Wright hypergeometric function and then use this theorem to evaluate some definite…
In this work we propose and analyse a numerical method for computing a family of highly oscillatory integrals with logarithmic singularities. For these quadrature rules we derive error estimates in terms of $N$, the number of nodes, $k$ the…
In this article it is proven the existence of integration of indefinite integrals as infinite derivative's series expansion. This also opens a new way to integrate a definite integral.
We propose an efficient approach for time integration of Klein-Gordon equations with highly oscillatory in time input terms. The new methods are highly accurate in the entire range, from slowly varying up to highly oscillatory regimes. Our…
In this paper, we shall prove the uniform sharp $L^p$ decay estimates for a class of oscillatory integral operators with polynomial phases. By this one-dimensional result, we can use the rotation method to obtain uniform sharp $L^p$…
Our purpose in this present paper is to investigate generalized integration formulas containing the extended generalized hypergeometric function and obtained results are expressed in terms of extended hypergeometric function. Certain…
Two approximations of the integral of a class of sinusoidal composite functions, for which an explicit form does not exist, are derived. Numerical experiments show that the proposed approximations yield an error that does not depend on the…
In this paper we generalize and improve a method for calculating the period of a classical oscillator and other integrals of physical interest, which was recently developed by some of the authors. We derive analytical expressions that prove…
A generalization of the definition of an oscillatory matrix based on the theory of cones is given in this paper. The positivity and simplicity of all the eigenvalues of a generalized oscillatory matrix are proved. The classes of generalized…
We prove genuinely multilinear weighted estimates for singular integrals in product spaces. The estimates complete the qualitative weighted theory in this setting. Such estimates were previously known only in the one-parameter situation.…
The goal of this Section is to formulate some of the basic results on the theory of integral equations and mention some of its applications. The literature of this subject is very large. Proofs are not given due to the space restriction.…
We present a method using contour integration to derive definite integrals and their associated infinite sums which can be expressed as a special function. We give a proof of the basic equation and some examples of the method. The advantage…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
This study is on small oscillations of a heavy symmetric top. A different method than previous works is applied, and differently from previous works, the explicit formulas for the amplitudes for oscillations are given. This method can be…
We prove sharp $L^2$ regularity results for classes of strongly singular Radon transfoms on the Heisenberg group by means of oscillatory integrals. We show that the problem in question can be effectively treated by establishing uniform…
The development of high-degree interpolation polynomials which use the values of the function and its subsequent derivatives is reformulated. Also, we present a variant of new formula in barycentric form.
The article presents the procedure of the index calculation for the elements of the algebra generated by one dimensional singular integral operators with discontinuous oscillating coefficients.
Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
Estimates of some integrals related to variations of smooth functions are presented.