Related papers: Exact Evaluation Of Some Highly Oscillatory Integr…

The sharp range of $L^p$-estimates for the class of H\"ormander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of…

Oscillatory integrals arise in many situations where it is important to obtain decay estimates which are stable under certain perturbations of the phase. Examining the structural problems underpinning these estimates leads one to consider…

We give an exact result about the asymptotic limit of an oscillatory integral whose phase contains a certain flat term. Corresponding to the real analytic phase case, one can see an essential difference in the behavior of the above…

In the present paper we derive a unified new integral whose integrand contains products of Fox $H$-function and a general class of polynomials having general arguments. A large number of integrals involving various simpler functions follow…

In the present study we highlight some results related to the oscillation for high order nonlinear generalized neutral difference equation in the following form \begin{equation*}…

In this paper we describe a general method to generate superoscillatory functions of several variables starting from a superoscillating sequence of one variable. Our results are based on the study of suitable infinite order differential…

An $n$th-order first derivative test for oscillatoric integrals is established. When the phase has a single stationary point, an $n$th-order asymptotic expansion of a weighted stationary phase integral is proved for arbitrary $n\geq1$. This…

Special cases of Weber-Schafheitlin type integrals are evaluated analytically.

The goal of this work is to determine whole classes of solitary wave solutions general for wave equations.

We give explicit expressions for higher order convolutions of Cauchy numbers, either as one single integral or in terms of the Stirling numbers of the first and second kinds.

We consider several possible approaches to evaluating an integral involving the digamma function and a related logarithmic series.

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.

The Riccati equation method is used to establish some new oscillatory criteria for the hamiltonian systems in a new direction, which is to break the positive definiteness restriction imposed on one of coefficients of the hamiltonian system.…

This note is a short survey of two topics: Archimedean zeta functions and Archimedean oscillatory integrals. We have tried to portray some of the history of the subject and some of its connections with similar devices in mathematics. We…

We develop two classes of composite moment-free numerical quadratures for computing highly oscillatory integrals having integrable singularities and stationary points. The first class of the quadrature rules has a polynomial order of…

Some finite series of harmonic numbers involving certain reciprocals are evaluated. Products of such reciprocals are expanded in a sum of the individual reciprocals, leading to a computer program. A list of examples is provided.

A variational and perturbative treatment is provided for a family of generalized spiked harmonic oscillator Hamiltonians H = -(d/dx)^2 + B x^2 + A/x^2 + lambda/x^alpha, where B > 0, A >= 0, and alpha and lambda denote two real positive…

In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of $\sinc$ functions. We then give a general formula to compute the integral on the real line of the…

We consider difference equations with several non-monotone deviating arguments and nonnegative coefficients. The deviations (delays and advances) are, generally, unbounded. Sufficient oscillation conditions are obtained in an explicit…

This paper deals with generalized elliptic integrals and generalized modular functions. Several new inequalities are given for these and related functions.